Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

A

Two objects m₁ and m₂ approach each other along a straight line with speeds v₁ and v₂ as shown. The objects collide and stick together.

What is the total change of linear momentum of the objects as a result of the collision? 

A. m₁v₁ + m₂v₂
B. m₁v₁ – m₂v₂ 
C. m₂v₂ – m₁v₁ 
D. zero

D

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

C

A projectile is fired at an angle to the horizontal. Air resistance is negligible. The path of the projectile is shown.

Which gives the magnitude of the horizontal component and the magnitude of the vertical component of the velocity of the projectile between O and P?

A

An elevator (lift) and its load have a total mass of 750 kg and accelerate vertically downwards at 2.0 m s^–2.

What is the tension in the elevator cable?

A.  1.5 kN
B.  6.0 kN
C.  7.5 kN
D.  9.0 kN

B

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

B

Candidate responses were divided between responses B (correct), D, and to a lesser extent, C. Many candidates appeared to focus on vertical velocity only or confused vertical velocity and acceleration values. This question had the highest discrimination index, suggesting that it would be a useful question for class discussion.

A ball undergoes an elastic collision with a vertical wall. Which of the following is equal to zero?

A. The change of the magnitude of linear momentum of the ball

B. The magnitude of the change of linear momentum of the ball

C. The rate of change of linear momentum of the ball

D. The impulse of the force on the ball

A

The graph shows the variation with time t of the force F acting on an object of mass 15 000 kg.

The object is at rest at t = 0.

What is the speed of the object when t = 30 s?

A.     0.18 m s^–1

B.     6 m s^–1

C.     12 m s^–1

D.     180 m s^–1

B

An object of weight W is falling vertically at a constant speed in a fluid. What is the magnitude of the drag force acting on the object? 

A. 0
B. $\frac{W}{2}$
C. W 
D. 2W

C

X and Y are two objects on a frictionless table connected by a string. The mass of X is 2 kg and the mass of Y is 4 kg. The mass of the string is negligible. A constant horizontal force of 12 N acts on Y.

What are the acceleration of Y and the magnitude of the tension in the string?

A

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

D

A rocket has just been launched vertically from Earth. The image shows the free-body diagram of the rocket. F₁ represents a larger force than F₂.

Which force pairs with F₁ and which force pairs with F₂, according to Newton’s third law?

B

A motor of input power 160 W raises a mass of 8.0 kg vertically at a constant speed of 0.50 m s^–1.

What is the efficiency of the system?

A.     0.63%

B.     25%

C.     50%

D.     100%

B

An object of mass $m$ strikes a vertical wall horizontally at speed $U$. The object rebounds from the wall horizontally at speed $V$.

What is the magnitude of the change in the momentum of the object?

A.  $0$

B.  $m\left(V-U\right)$

C.  $m\left(U-V\right)$

D.  $m\left(U+V\right)$

D

Two forces act along a straight line on an object that is initially at rest. One force is constant; the second force is in the opposite direction and proportional to the velocity of the object.

What is correct about the motion of the object?

A. The acceleration increases from zero to a maximum.

B. The acceleration increases from zero to a maximum and then decreases.

C. The velocity increases from zero to a maximum.

D. The velocity increases from zero to a maximum and then decreases.

C

The mass at the end of a pendulum is made to move in a horizontal circle of radius r at constant speed. The magnitude of the net force on the mass is F.

What is the direction of F and the work done by F during half a revolution?

A

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

A

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

B

A sky diver is falling at terminal speed when she opens her parachute. What are the direction of her velocity vector and the direction of her acceleration vector before she reaches the new terminal speed?

C

The graph shows the variation of velocity of a body with time along a straight line.

What is correct for this graph?

A. The maximum acceleration is at P.

B. The average acceleration of the body is given by the area enclosed by the graph and time axis.

C. The maximum displacement is at Q.

D. The total displacement of the body is given by the area enclosed by the graph and time axis.

D

A student of weight 600N climbs a vertical ladder 6.0m tall in a time of 8.0s. What is the power developed by the student against gravity?

A. 22W
B. 45W 
C. 220W 
D. 450W

D

A boy runs along a straight horizontal track. The graph shows how his speed v varies with time t.

After 15 s the boy has run 50 m. What is his instantaneous speed and his average speed when t = 15 s?

C

Two forces of magnitude 12 N and 24 N act at the same point. Which force cannot be the resultant of these forces?

A. 10 N

B. 16 N

C. 19 N

D. 36 N

A

An electron has a linear momentum of 4.0 × 10⁻²⁵ kg m s⁻¹. What is the order of magnitude of the kinetic energy of the electron?

A. 10⁻⁵⁰ J

B. 10⁻³⁴ J

C. 10⁻¹⁹ J

D. 10⁶ J

C

Two masses $m_1$ and $m_2$ are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.

Mass $m_2$ accelerates downwards at $\frac{g}{2}$. What is $\frac{m_1}{m_2}$?
A.  $\frac{1}{3}$

B.  $\frac{1}{2}$

C.  2

D.  3

A

With a low difficulty index for both, this question was challenging for both HL and SL candidates. Option B was the most common (incorrect) answer, and only a small number of candidates correctly selected option A. This question would be a useful teaching tool for students, as they consider the relationship between variables without numeric substitution.

A net force acts on a body. Which characteristic of the body will definitely change?

A.  Speed

B.  Momentum

C.  Kinetic energy

D.  Direction of motion

B

A table-tennis ball of mass 3 g is fired with a speed of 10 m s^-1 from a stationary toy gun of mass 0.600 kg. The gun and ball are an isolated system.

What are the recoil speed of the toy gun and the total momentum of the system immediately after the gun is fired?

A

This question gives good discrimination at both levels with the correct response, A, being the most popular at HL. Response B was second most popular at HL and most popular by a small margin at SL, however a significant number of candidates chose the other responses at both levels. Realising the gun and ball are initially at rest and momentum must be conserved leads to a zero momentum after firing, immediately removing options B and D.

An object is thrown upwards. The graph shows the variation with time t of the velocity v of the object.

What is the total displacement at a time of 1.5 s, measured from the point of release?

A. 0 m

B. 1.25 m

C. 2.50 m

D. 3.75 m

B

The graph shows the variation with time t of the velocity of an object.

What is the variation with time t of the acceleration of the object?

A

A ball is thrown vertically downwards with an initial speed of 4.0 m s⁻¹. The ball hits the ground with a speed of 16 m s⁻¹. Air resistance is negligible. What is the time of fall and what is the distance travelled by the ball?

D

The initial kinetic energy of a block moving on a horizontal floor is 48 J. A constant frictional force acts on the block bringing it to rest over a distance of 2 m. What is the frictional force on the block?

A.  24 N

B.  48 N

C.  96 N

D.  192 N

A

A graph shows the variation of force acting on an object moving in a straight line with distance moved by the object. Which area represents the work done on the object during its motion from P to Q?

A.  X
B.  Y
C.  Y + Z
D.  X + Y + Z

C

A car travelling at a constant velocity covers a distance of 100 m in 5.0 s. The thrust of the engine is 1.5 kN. What is the power of the car?

A.  0.75 kW
B.  3.0 kW
C.  7.5 kW
D.  30 kW

D

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

A

An object is pushed from rest by a constant net force of 100 N. When the object has travelled 2.0 m the object has reached a velocity of 10 m s⁻¹.

What is the mass of the object?

A.  2 kg

B.  4 kg

C.  40 kg

D.  200 kg

B

A runner starts from rest and accelerates at a constant rate throughout a race. Which graph shows the variation of speed v of the runner with distance travelled s?

A

The efficiency of an electric motor is 20 %. When lifting a body 500 J of energy are wasted. What is the useful work done by the motor?

A.  100 J

B.  125 J

C.  250 J

D.  400 J

B

An elevator (lift) and its load accelerate vertically upwards.

Which statement is correct in this situation?

A.  The net force on the load is zero.

B.  The tension in the cable is equal but opposite to the combined weight of the elevator and its load.

C.  The normal reaction force on the load is equal but opposite to the force on the elevator from the load.

D.  The elevator and its load are in translational equilibrium.

C

Two balls X and Y with the same diameter are fired horizontally with the same initial momentum from the same height above the ground. The mass of X is greater than the mass of Y. Air resistance is negligible.

What is correct about the horizontal distances travelled by X and Y and the times taken by X and Y to reach the ground?

C

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

B

Two identical boxes containing different masses are sliding with the same initial speed on the same horizontal surface. They both come to rest under the influence of the frictional force of the surface. How do the frictional force and acceleration of the boxes compare?

B

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

A

An object is released from rest in the gravitational field of the Earth. Air resistance is negligible. How far does the object move during the fourth second of its motion?

A.  15 m
B.  25 m
C.  35 m
D.  45 m

C

Child X throws a ball to child Y. The system consists of the ball, the children and the Earth. What is true for the system when the ball has been caught by Y?

A.     The momentum of child Y is equal and opposite to the momentum of child X.

B.     The speed of rotation of the Earth will have changed.

C.     The ball has no net momentum while it is in the air.

D.     The total momentum of the system has not changed.

D

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

A

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

C

Candidate responses were largely divided between responses C and D, suggesting some confusion around the direction of frictional force in a rotating object (vs. linear motion).

A ball rolls on the floor towards a wall and rebounds with the same speed and at the same angle to the wall.

What is the direction of the impulse applied to the ball by the wall?

D

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

B

With a lower difficulty index for SL candidates than for HL candidates, this question asked students to recognize the relationship between variables in a kinematics equation. For both groups, option C (incorrect) was most frequently selected, as candidates struggled to show the relationship between U and the change in frictional force. This question would be a useful teaching tool, as results here suggest candidates should spend more time working with equations without numerical substitutions.

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

D

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

Calculate the speed of the probe in terms of $c$, relative to Earth.

B

$u=\frac{0.5c+0.8c}{1+{\displaystyle \frac{0.5c\times 0.8c}{c^{\mathit{2}}}}}$ ✓

$u=0.93\mathrm{c}$ ✓

Allow all negative signs for velocities

Award [2] marks for a bald correct answer

An astronaut is moving at a constant velocity in the absence of a gravitational field when he throws a tool away from him.

What is the effect of throwing the tool on the total kinetic energy of the astronaut and the tool and the total momentum of the astronaut and the tool?

D

A ball of mass m strikes a vertical wall with a speed v at an angle of θ to the wall. The ball rebounds at the same speed and angle. What is the change in the magnitude of the momentum of the ball?

A. 2 mv sin θ
B. 2 mv cos θ
C. 2 mv 
D. zero

B

Momentum is a vector quantity so the angle and the direction are both relevant to the answer. Hence C and D can be eliminated. If θ = 900, then the ball is just rolling down the wall and there is no change in momentum. Hence B is correct (cos900 = 0).

A ball is thrown vertically upwards. Air resistance is negligible. What is the variation with time t of the kinetic energy E_k of the ball?

D

A ball of mass 0.2 kg strikes a force sensor and sticks to it. Just before impact the ball is travelling horizontally at a speed of 4.0 m s^–1. The graph shows the variation with time t of the force F recorded by the sensor.

What is F_max?

A.  2 N

B.  4 N

C.  20 N

D.  40 N

D

An object, initially at rest, is accelerated by a constant force. Which graphs show the variation with time t of the kinetic energy and the variation with time t of the speed of the object?

A

Two identical blocks, each of mass m and speed v, travel towards each other on a frictionless surface.

The blocks undergo a head-on collision. What is definitely true immediately after the collision?

A. The momentum of each block is zero.

B. The total momentum is zero.

C. The momentum of each block is 2mv.

D. The total momentum is 2mv.

B

An object has a weight of 6.10 × 10² N. What is the change in gravitational potential energy of the object when it moves through 8.0 m vertically?

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

B

At SL, more candidates chose C with B the second most popular response. This question was about significant figures and candidates should be reminded that on the multiple choice paper they are not expected to perform detailed calculations. In this case 6.10 (to 3 sig figs) times 8.0 (to 2 sig figs) produces an answer to 2 sig figs giving B as the correct response. All answers are equivalent from a numerical point of view with the difference being the number of sig figs used.

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

C

A truck has an initial speed of 20 m s^–1. It decelerates at 4.0 m s^–2. What is the distance taken by the truck to stop?

A.   2.5 m

B.   5.0 m

C.   50 m

D.   100 m

C

A uniform ladder resting in equilibrium on rough ground leans against a smooth wall. Which diagram correctly shows the forces acting on the ladder?

B

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

D

An object is projected vertically upwards at time t = 0. Air resistance is negligible. The object passes the same point above its starting position at times 2 s and 8 s.

If g = 10 m s^–2, what is the initial speed of the object?

A.     50

B.     30

C.     25

D.     4 

A

A ball of mass m is thrown with an initial speed of u at an angle θ to the horizontal as shown. Q is the highest point of the motion. Air resistance is negligible.

What is the momentum of the ball at Q?

A.     zero

B.     mu cosθ

C.     mu

D.     mu sinθ

B

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

C

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

B

A ball is tossed vertically upwards with a speed of 5.0 m s^–1. After how many seconds will the ball return to its initial position?

A.  0.50 s

B.  1.0 s

C.  1.5 s

D.  2.0 s

B

A cube slides down the surface of a ramp at a constant velocity. What is the magnitude of the frictional force that acts on the cube due to the surface?

A. The weight of the cube

B. The component of weight of the cube parallel to the plane

C. The component of weight of the cube perpendicular to the plane

D. The component of the normal reaction at the surface parallel to the plane

B

Two identical boxes are stored in a warehouse as shown in the diagram. Two forces acting on the top box and two forces acting on the bottom box are shown.

Which is a force pair according to Newton’s third law?

A. 1 and 2

B. 3 and 4

C. 2 and 3

D. 2 and 4

C

The road from city X to city Y is 1000 km long. The displacement is 800 km from X to Y.

What is the distance travelled from Y to X and the displacement from Y to X?

D

A boat with an output engine power of 15 kW moves through water at a speed of 10 m s^-1. What is the resistive force acting on the boat?

A. 0.15 kN

B. 0.75 kN

C. 1.5 kN

D. 150 kN

C

The graph shows the variation with distance of a horizontal force acting on an object. The object, initially at rest, moves horizontally through a distance of $50 \text{m}$.

A constant frictional force of $2.0 \text{N}$ opposes the motion. What is the final kinetic energy of the object after it has moved $50 \text{m}$?

A. $100 \text{J}$

B. $500 \text{J}$

C. $600 \text{J}$

D. $1100 \text{J}$

B

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

B

A person with a weight of $600 \text{N}$ stands on a scale in an elevator.

What is the acceleration of the elevator when the scale reads $900 \text{N}$?

A.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

B.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

C.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

D.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

D

A moving system undergoes an explosion. What is correct for the momentum of the system and the kinetic energy of the system when they are compared immediately before and after the explosion?

A

A climber of mass m slides down a vertical rope with an average acceleration a. What is the average frictional force exerted by the rope on the climber?

A. mg

B. m(g + a)

C. m(g – a)

D. ma

C

A box is accelerated to the right across rough ground by a horizontal force F_a. The force of friction is F_f. The weight of the box is F_g and the normal reaction is F_n. Which is the free-body diagram for this situation?

D

The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension $x$ is $E$. What is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$?

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

D

A projectile is fired horizontally from the top of a cliff. The projectile hits the ground 4 s later at a distance of 2 km from the base of the cliff. What is the height of the cliff?

A.  40 m

B.  80 m

C.  120 m

D.  160 m

B

A tennis ball is released from rest at a height h above the ground. At each bounce 50 % of its kinetic energy is lost to its surroundings. What is the height reached by the ball after its second bounce?

A.  $\frac{h}{8}$

B.  $\frac{h}{4}$

C.  $\frac{h}{2}$

D.  zero

B

An object is released from a stationary hot air balloon at height h above the ground.

An identical object is released at height h above the ground from another balloon that is rising at constant speed. Air resistance is negligible. What does not increase for the object released from the rising balloon?

A. The distance through which it falls

B. The time taken for it to reach the ground

C. The speed with which it reaches the ground

D. Its acceleration

D

An object of mass $8.0 \mathrm{kg}$ is falling vertically through the air. The drag force acting on the object is $60 \mathrm{N}$. What is the best estimate of the acceleration of the object?

A.  Zero

B.  $2.5 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $7.5 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

B

A car takes 20 minutes to climb a hill at constant speed. The mass of the car is 1200 kg and the car gains gravitational potential energy at a rate of 6.0 kW. Take the acceleration of gravity to be 10 m s⁻². What is the height of the hill?

A. 0.6 m

B. 10 m

C. 600 m

D. 6000 m

C

A stone is thrown downwards from the edge of a cliff with a speed of 5.0 m s^–1. It hits the ground 2.0 s later. What is the height of the cliff?

A. 20 m

B. 30 m

C. 40 m

D. 50 m

B

This question was well answered by the majority of candidates and had a high discrimination index.

A person is standing at rest on the ground and experiences a downward gravitational force W and an upward normal force from the ground N. Which, according to Newton’s third law, is the force that together with W forms a force pair?

A. The gravitational force W acting upwards on the ground.

B. The gravitational force W acting upwards on the person.

C. The normal force N acting upwards on the person.

D. The normal force N acting downwards on the ground.

A

An increasing force acts on a metal wire and the wire extends from an initial length l₀ to a new length l. The graph shows the variation of force with length for the wire. The energy required to extend the wire from l₀ to l is E.

The wire then contracts to half its original extension.

What is the work done by the wire as it contracts?

A.     0.25E

B.     0.50E

C.     0.75E

D.     E 

C

The variation with time t of the acceleration a of an object is shown.

What is the change in velocity of the object from t = 0 to t = 6 s?

A. 6 m s^–1

B. 8 m s^–1

C. 10 m s^–1

D. 14 m s^–1

C

Two blocks X and Y rest on a frictionless horizontal surface as shown. A horizontal force is now applied to the larger block and the two blocks move together with the same speed and acceleration.

Which free-body diagram shows the frictional forces between the two blocks?

A

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

A

Response A was the most common (correct) response, however response D was a significant distractor for candidates who took momentum to be a scalar quantity.

A block of weight W slides down a ramp at constant velocity. A friction force F acts between the bottom of the block and the surface of the ramp. A normal reaction N acts between the ramp and the block. What is the free-body diagram for the forces that act on the block?

D

An object of mass 1.0 kg hangs at rest from a spring. The spring has a negligible mass and the spring constant k is 20 N m⁻¹

What is the elastic potential energy stored in the spring?

A.  1.0 J

B.  2.5 J

C.  5.0 J

D.  10 J

B

A large stone is dropped from a tall building. What is correct about the speed of the stone after 1 s?

A. It is decreasing at increasing rate.

B. It is decreasing at decreasing rate.

C. It is increasing at increasing rate.

D. It is increasing at decreasing rate.

D

Two stationary objects of mass 1kg and 2kg are connected by a thread and suspended from a spring.

The thread is cut. Immediately after the cut, what are the magnitudes of the accelerations of the objects in terms of the acceleration due to gravity g?

D

An object is sliding from rest down a frictionless inclined plane. The object slides 1.0 m during the first second.

What distance will the object slide during the next second?

A.  1.0 m

B.  2.0 m

C.  3.0 m

D.  4.9 m

C

The correct response, option C was the most popular chosen at HL but at SL significantly more candidates chose options A or B. The difficulty index of 21 and discrimination index of 0.27 at SL indicates that students found the question to be hard with lower discrimination between stronger and weaker candidates. It is felt that those who chose option A did not realise the block was accelerating down the slope, whereas those choosing B did but were unable to calculate the acceleration correctly.

An inelastic collision occurs between two bodies in the absence of external forces.

What must be true about the total momentum of the two bodies and the total kinetic energy of the two bodies during this interaction?

A.  Only momentum is conserved.
B.  Only kinetic energy is conserved.
C.  Both momentum and kinetic energy are conserved.
D.  Neither momentum nor kinetic energy are conserved.

A

An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a straight line with a force of 10 N through a distance d.

The resultant force acting on the object throughout d is 6.0 N.

What is the value of the sliding coefficient of friction $\mu$ between the surface and the object and what is the acceleration a of the object?

A

There is no evidence that candidates were disadvantaged by the use of sliding friction rather than dynamic friction with the correct option being the most popular.

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

B

This question was generally well answered by both HL and SL candidates and had a mid-range difficulty index (indicating an easier question). Option D was an effective distractor for candidates calculating the horizontal range rather than the displacement. Candidates are encouraged to read the questions carefully to ensure it is clear what each question is asking for.

Two trolleys of equal mass travel in opposite directions as shown.

The trolleys collide head-on and stick together.

What is their velocity after the collision?

A.  1 m s⁻¹

B.  2 m s⁻¹

C.  5 m s⁻¹

D.  10 m s⁻¹

A

The majority of SL candidates selected option B, finding the difference in velocity but neglecting to recognize that mass will have doubled. This question had a relatively high discrimination index suggesting more able candidates had greater success demonstrating this recognition.

Which of the formulae represents Newton’s second law?

A.  $\frac{\text{mass}}{\text{volume}}$

B.  $\frac{\text{work}}{\text{displacement}}$

C.  $\frac{\text{change of momentum}}{\text{time}}$

D.  $\text{pressure}\times \text{area}$

C

This question was very well answered by SL candidates, as demonstrated by the high difficulty index.

A net force $F$ acts on an object of mass $m$ that is initially at rest. The object moves in a straight line. The variation of $F$ with the distance $s$ is shown.

What is the speed of the object at the distance $s_1$?

A.  $\sqrt{\frac{F_1{s}_1}{2m}}$

B.  $\sqrt{\frac{F_1{s}_1}{m}}$

C.  $\sqrt{\frac{2F_1{s}_1}{m}}$

D.  $\sqrt{\frac{4F_1{s}_1}{m}}$

B

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

D

Option A was the most common (incorrect) response among both HL and SL candidates, suggesting that candidates were looking for a curve representing speed rather than kinetic energy against distance. A low discrimination index suggests that both high and low achieving students were caught by this effective distractor.

A projectile is launched upwards at an angle θ to the horizontal with an initial momentum p₀ and an initial energy E₀. Air resistance is negligible. What are the momentum and total energy of the projectile at the highest point of the motion?

A

Two forces act on an object in different directions. The magnitudes of the forces are 18 N and 27 N. The mass of the object is 9.0 kg. What is a possible value for the acceleration of the object?

A. 0 m s⁻²

B. 0.5 m s⁻²

C. 2.0 m s⁻²

D. 6.0 m s⁻²

C

Three forces act on a block which is sliding down a slope at constant speed. $W$ is the weight, $R$ is the reaction force at the surface of the block and $F$ is the friction force acting on the block.

In this situation

A.  there must be an unbalanced force down the plane.

B.  $W=R$.

C.  $F=W$.

D.  the resultant force on the block is zero.

D

The distances between successive positions of a moving car, measured at equal time intervals, are shown.

The car moves with

A.     acceleration that increases linearly with time.

B.     acceleration that increases non-linearly with time.

C.     constant speed.

D.     constant acceleration.

D

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

A

Many candidates (incorrectly) selected response B, perhaps neglecting the changing value of force over time.

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

B

Two boxes in contact are pushed along a floor with a force F. The boxes move at a constant speed. Box X has a mass m and box Y has a mass 2m.

What is the resultant force acting on Y?
A.  0
B.  $\frac{F}{2}$
C.  F
D.  2F

A

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

A

The variation of the displacement of an object with time is shown on a graph. What does the area under the graph represent?

A. No physical quantity

B. Velocity

C. Acceleration

D. Impulse

A

The graph shows how the position of an object varies with time in the interval from 0 to 3 s.

At which point does the instantaneous speed of the object equal its average speed over the interval from 0 to 3 s?

C

Two blocks of different masses are released from identical springs of elastic constant k = 100 Nm⁻¹, initially compressed a distance Δx = 0.1 m. Block X has a mass of 1 kg and block Y has a mass of 0.25 kg.

What are the velocities of the blocks when they leave the springs?

C

Most candidates chose the correct answer confirming this was not problematic.

The graph shows the variation of speed v of an object with time t.

Which graph shows how the distance s travelled by the object varies with t?

B

An electric motor of efficiency 0.75 is connected to a power supply with an emf of 20 V and negligible internal resistance. The power output of the motor is 120 W. What is the average current drawn from the power supply?

A.  3.1 A

B.  4.5 A

C.  6.0 A

D.  8.0 A

D

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

C

Even though over half the candidates are choosing the correct response it has a low discrimination index. Many are choosing D indicating that they forgot to take the velocity upward as negative.