Space, Time, and Motion — Free IB Physics SL Practice Questions

1FoundationMCQWork done by a force1 markPaper 1~2 min

A satellite travels at constant speed in a circular orbit of radius

r

around Earth. At every point in the orbit, the gravitational force on the satellite has magnitude

F

and is directed toward the centre of Earth. What is the net work done by the gravitational force on the satellite during one complete orbit?

Solutions

2FoundationMCQWork done by a force1 markPaper 1~2 min

A box slides down a frictionless inclined plane of length

3.0\text{ m}

inclined at

30°

to the horizontal. The weight of the box is

50\text{ N}

. What is the work done by the weight of the box as it slides from the top to the bottom of the plane?

Solutions

3FoundationMCQWork done by a force1 markPaper 1~2 min

A force

F

acts on an object in the direction of motion. The graph shows

F

varying linearly from

10\text{ N}

at

s = 0

to

0\text{ N}

at

s = 4.0\text{ m}

. What is the work done by the force over this displacement?

Solutions

4FoundationMCQKinetic and potential energy1 markPaper 1~2 min

A roller coaster car of mass 500 kg starts from rest at point A, which is 40 m above the ground. It travels along a frictionless track to point B, which is 15 m above the ground. What is the speed of the car at point B?

Solutions

5FoundationMCQKinetic and potential energy1 markPaper 1~2 min

A pendulum bob of mass

0.20\text{ kg}

is released from rest a point where the string, of length

1.5\text{ m}

, makes angle of

60°

with the vertical. What is the speed of the bob as it passes through the lowest point of its swing?

Solutions

6FoundationMCQScalars and vectors1 markPaper 1~2 min

A cyclist travels at a constant speed of

6.0 \text{ m s}^{-1}

north for

5.0 \text{ s}

, then at a constant speed of

8.0 \text{ m s}^{-1}

east for

5.0 \text{ s}

. What is the magnitude of the average velocity of the cyclist for the entire journey?

Solutions

7MasteryMCQGraphical analysis of motion1 markPaper 1~2 min

A cyclist travels along a straight road. Her velocity–time graph consists of a straight line from

(0\ \text{s},\ 0\ \text{m s}^{-1})

to

(5.0\ \text{s},\ 10\ \text{m s}^{-1})

, a horizontal line at

10\ \text{m s}^{-1}

from

t = 5.0\ \text{s}

to

t = 15\ \text{s}

, and a straight line from

(15\ \text{s},\ 10\ \text{m s}^{-1})

to

(20\ \text{s},\ 0\ \text{m s}^{-1})

. What is the total displacement of the cyclist?

Solutions

8FoundationMCQScalars and vectors1 markPaper 1~2 min

A sailboat is acted on by a wind force of

30 \text{ N}

directed due east and a water current force of

40 \text{ N}

directed due north. What is the magnitude of the resultant of these two forces?

Solutions

9FoundationMCQGraphical analysis of motion1 markPaper 1~2 min

A cyclist travels along a straight road. Her velocity–time graph is a horizontal straight line at

v = 6 \ \text{m s}^{-1}

for

0 \leq t \leq 8 \ \text{s}

. What is the displacement of the cyclist during this 8-second interval?

Solutions

10MasteryMCQGraphical analysis of motion1 markPaper 1~2 min

A parachutist descends vertically from rest. Taking downward as positive, her velocity increases uniformly from

0\ \text{m s}^{-1}

at

t = 0\ \text{s}

to

19.6\ \text{m s}^{-1}

at

t = 2.0\ \text{s}

, then remains constant at

19.6\ \text{m s}^{-1}

until

t = 5.0\ \text{s}

. What is her displacement between

t = 0

and

t = 5.0\ \text{s}

?

Solutions

11FoundationMCQForce, mass, and acceleration1 markPaper 1~2 min

A car of mass

1200 \text{ kg}

is travelling at

20 \text{ m s}^{-1}

along a straight horizontal road. The driver applies the brakes, exerting a constant braking force of

4800 \text{ N}

on the car. What is the magnitude of the deceleration of the car?

Solutions

12MasteryMCQMomentum and impulse1 markPaper 1~2 min

A tennis ball of mass

0.050\ \text{kg}

travels horizontally at

30\ \text{m s}^{-1}

toward a wall. It rebounds horizontally at

20\ \text{m s}^{-1}

in the opposite direction after a contact time of

0.010\ \text{s}

. What is the magnitude of the average force exerted by the wall on the ball?

Solutions

13MasteryMCQConservation of momentum1 markPaper 1~2 min

A car of mass

1200 \text{ kg}

travelling at

15 \text{ m s}^{-1}

east collides head-on with a truck of mass

1600 \text{ kg}

travelling at

10 \text{ m s}^{-1}

west. The vehicles lock together on impact. What is the velocity of the combined wreckage immediately after the collision?

Solutions

14FoundationMCQForce, mass, and acceleration1 markPaper 1~2 min

A block of mass

2.0 \text{ kg}

is pulled along a rough horizontal surface by a single horizontal force of

10 \text{ N}

. The coefficient of kinetic friction between the block and the surface is

0.15

. What is the magnitude of the acceleration of the block? (Take

g = 10 \text{ m s}^{-2}

.)

Solutions

15MasteryMCQMomentum and impulse1 markPaper 1~2 min

A hockey puck of mass

0.45 \text{ kg}

slides on frictionless ice at

12 \text{ m s}^{-1}

and collides head-on with a stationary puck of mass

0.18 \text{ kg}

. After the collision, the

0.45 \text{ kg}

puck moves in the same direction at

4.0 \text{ m s}^{-1}

. What is the speed of the

0.18 \text{ kg}

puck immediately after the collision?

Solutions

16FoundationSAQ-SPower and efficiency5 marksPaper 2~8 min

A wind turbine has blades of radius 35 m. The density of air is

1.2 \text{ kg m}^{-3}

. The wind speed is

12 \text{ m s}^{-1}

. The kinetic energy of air passing through the area swept by the blades per second is given by

\frac{1}{2}\rho A v^3

, where

\rho

is the density of air,

A

is the swept area, and

v

is the wind speed. The turbine converts 40% of this kinetic energy into electrical energy per second.

(a)

(i) State what is meant by the efficiency of the wind turbine. [1]
(ii) State one reason why the efficiency of a wind turbine must always be less than 100%. [1 mark]

(b)

Calculate the electrical power output of the turbine. [3 marks]

Solutions

17MasterySAQ-SConservation of mechanical energy5 marksPaper 2~8 min

A child of mass 25.0 kg slides down a frictionless slide from rest at point A, which is 3.20 m above the ground. At point B, the child is 1.20 m above the ground.

g = 9.81 \ \text{m s}^{-2}

(a)

State one condition, other than the absence of friction, that is necessary for mechanical energy to be conserved as the child slides from A to B. [1 mark]

(b)

Calculate the speed of the child at point B. [2 marks]

(c)

The slide is now roughened so that friction acts between the child and the slide. The friction force does

-85.0 \ \text{J}

of work on the child between A and B. Explain why the speed at B is less than your answer in (b), and determine by how much the kinetic energy at B is reduced compared to the frictionless case. [2 marks]

Solutions

18ChallengeSAQ-LConservation of mechanical energy7 marksPaper 2~11 min

A roller coaster car of mass 500 kg starts from rest at point A, which is 45 m above the ground. The track descends to point B at ground level, rises to point C at 20 m above the ground, and then enters a vertical circular loop of radius 12 m. The bottom of the loop is at ground level. Assume no energy losses due to friction.

(a)

State the assumption required to apply conservation of mechanical energy, and determine the speed of the car at point B. [2 marks]

(b)

Determine the speed of the car at point D, the top of the loop. [2 marks]

(c)

Explain why a minimum speed is required at point D for the car to maintain contact with the track. [1 mark]

(d)

Calculate the minimum speed required at point D, and hence evaluate whether the car successfully completes the loop. [2 marks]

Solutions

19FoundationSAQ-SPower and efficiency8 marksPaper 2~12 min

A student lifts a 15 kg box vertically from the ground to a shelf 2.0 m high in 3.0 seconds. The student then slides the same box horizontally across a rough floor over a distance of 5.0 m in 4.0 seconds. The coefficient of kinetic friction between the box and the floor is 0.30.

g = 9.81 \text{ m s}^{-2}

(a)

State what is meant by a non-conservative force and identify which force in this question is non-conservative. [2 marks]

(b)

Calculate the total work done by the student against all resistive forces during the entire 7.0 s of activity. [3 marks]

(c)

The student claims that the average power output during the pushing phase alone is greater than during the lifting phase alone. Determine whether this claim is correct. [3 marks]

Solutions

20MasterySAQ-SConservation of mechanical energy7 marksPaper 2~11 min

A pendulum consists of a bob of mass 0.500 kg attached to a light inextensible string of length 2.00 m. The bob is displaced so that the string makes an angle of 30.0° with the vertical and is then released from rest.

g = 9.81 \text{ m s}^{-2}, \quad \cos 30.0° = 0.866

(a)

State what is meant by the conservation of mechanical energy. [1 mark]

(b)

Show that the vertical height through which the bob descends from its release point to the lowest point of its swing is approximately 0.27 m. [2 marks]

(c)

Calculate the speed of the bob at the lowest point of its swing. [2 marks]

(d)

The pendulum is released again under the same conditions, but air resistance is now significant. Explain why the bob does not rise to its original height on the other side of the swing. [2 marks]

Solutions

21MasterySAQ-SDisplacement, velocity, and acceleration7 marksPaper 2~11 min

A train moves along a straight track. The velocity–time graph for the train over a

50 \text{ s}

journey is shown below. The graph shows three sections: - Section 1 — straight line from

(0,\ 0)

to

(20,\ 30)

- Section 2 — horizontal line from

(20,\ 30)

to

(40,\ 30)

- Section 3 — straight line from

(40,\ 30)

to

(50,\ 0)

The vertical axis is labelled

v \ / \ \text{m s}^{-1}

(range

0

to

35

) and the horizontal axis is labelled

t \ / \ \text{s}

(range

0

to

50

).

(a)

Calculate the acceleration of the train during Section 1 and during Section 3. [2 marks]

(b)

Determine the total displacement of the train over the entire

50 \text{ s}

journey. [2 marks]

(c)

The driver claims the train travelled a total distance of more than

1.1 \text{ km}

during this journey. Evaluate this claim, justifying why distance and displacement are equal in this case. [3 marks]

Solutions

22MasterySAQ-SScalars and vectors7 marksPaper 2~11 min

A runner completes a route: 400 m east, then 300 m north. The total time taken is 200 s.

(a)

State the total distance travelled by the runner. [1 mark]

(b)

Calculate the magnitude and direction of the runner's displacement from the starting point. [2 marks]

(c)

Calculate the average speed and the average velocity of the runner for this route. [2 marks]

(d)

The runner claims that average speed and average velocity are the same quantity expressed in different units. Deduce, using your answers to (b) and (c), whether this claim is correct. *You may use:

c^2 = a^2 + b^2

* [2 marks]

Solutions

23ChallengeSAQ-LGraphical analysis of motion7 marksPaper 2~11 min

A student drops a ball from rest at a height of

2.00\ \text{m}

above a motion sensor placed on the floor. The ball falls, bounces once off the floor, rises to a maximum height of

1.20\ \text{m}

, and is then caught. Take

g = 9.81\ \text{m s}^{-2}

acting downward. Define upward as positive throughout.

(a)

Determine the time taken for the ball to fall from rest to the floor. [2 marks]

(b)

(i) Determine the speed of the ball immediately before it strikes the floor. [1]
(ii) Determine the speed of the ball immediately after it leaves the floor following the bounce. [1 mark]

(c)

The ball has mass

m

. Using your values from (i) and
(ii), evaluate whether the collision of the ball with the floor is perfectly elastic. Justify your answer quantitatively in terms of kinetic energy. [3 marks]

Solutions

24ChallengeSAQ-LDisplacement, velocity, and acceleration7 marksPaper 2~11 min

A rocket sled is tested on a straight horizontal track. The velocity of the sled is shown on the graph described below. From

t = 0

to

t = 5.0

s, the velocity increases linearly from

0

to

120 \ \text{m s}^{-1}

. From

t = 5.0

s to

t = 10.0

s, the velocity decreases linearly from

120 \ \text{m s}^{-1}

to

40 \ \text{m s}^{-1}

.

(a)

Determine the acceleration of the sled during the first

5.0

s. [2 marks]

(b)

Determine the total displacement of the sled from

t = 0

to

t = 10.0

s, using areas under the velocity–time graph. [3 marks]

(c)

Evaluate whether the arithmetic mean of the initial and final velocities gives the correct average velocity for the full

10.0

s interval. Support your answer with a calculated value. [2 marks]

Solutions

25MasterySAQ-SGraphical analysis of motion7 marksPaper 2~11 min

A cyclist travels along a straight road. The velocity-time graph of the cyclist is shown below.

(a)

Identify the type of acceleration experienced by the cyclist during the first 8 seconds, and state one piece of evidence from the graph that supports your answer. [2 marks]

(b)

Calculate the acceleration of the cyclist during the time interval

t = 8\ \text{s}

to

t = 20\ \text{s}

. [2 marks]

(c)

Determine the total distance travelled by the cyclist over the full 20 seconds. [2 marks]

(d)

Explain whether the magnitude of the average velocity equals the average speed over the 20-second interval. [1 mark]

Solutions

26ChallengeSAQ-LNewton’s laws of motion7 marksPaper 2~11 min

A rocket-powered sled is used to test the effects of high acceleration on humans. The sled has a total mass of 620 kg, including the test subject. The rocket engine provides a constant forward thrust of 8400 N. A constant resistive force of 1200 N acts on the sled throughout its motion.

(a)

State the net force acting on the sled while the engine is firing. [1 mark]

(b)

Determine the acceleration of the sled while the engine is firing. [2 marks]

(c)

The engine fires for 4.0 s from rest and then suddenly fails, so that the thrust drops to zero. The resistive force remains constant at 1200 N. Determine the distance the sled travels from the moment the engine fails until the sled comes to rest. [2 marks]

(d)

The rocket engine operates by expelling exhaust gases backwards at high speed. Explain, using Newton's third law of motion, how the expelled gases produce a forward thrust on the sled. [1] (e) Evaluate whether the same engine could accelerate the sled if it were operating in the vacuum of space, where the resistive force is zero. [1 mark]

Solutions

27MasterySAQ-SNewton’s laws of motion6 marksPaper 2~9 min

A small rocket of total mass 0.80 kg rests on a horizontal frictionless surface. The rocket engine produces a constant thrust of 2.0 N for 3.0 s, after which the engine shuts off. The rocket starts from rest.

(a)

State the motion of the rocket after the engine shuts off, with reference to Newton's first law. [1 mark]

(b)

Calculate the acceleration of the rocket while the engine is firing. [2 marks]

(c)

Calculate the speed of the rocket at the moment the engine shuts off. [1 mark]

(d)

In practice, the rocket burns fuel during firing, so its total mass decreases. The thrust remains 2.0 N throughout. Deduce and explain whether the actual final speed is greater than, equal to, or less than your answer in (c). [2 marks]

Solutions

28ChallengeSAQ-LNewton’s laws of motion7 marksPaper 2~11 min

A person of mass 70 kg stands on a bathroom scale inside an elevator. The elevator accelerates upward from rest at

2.0 \ \text{m s}^{-2}

, then travels upward at constant speed, and finally decelerates at

1.5 \ \text{m s}^{-2}

before coming to rest.

g = 9.81 \ \text{m s}^{-2}

(a)

State the physical quantity measured by the bathroom scale. [1 mark]

(b)

Determine the scale reading during the upward acceleration phase. [2 marks]

(c)

Determine the scale reading during the deceleration phase. [2 marks]

(d)

The elevator cable then breaks and the elevator enters free fall. Deduce the scale reading under these conditions, justifying your answer by applying Newton's second law to the person. [2 marks]

Solutions

29ChallengeSAQ-LNewton’s laws of motion9 marksPaper 2~14 min

Data

g = 9.81\ \text{m s}^{-2}

Two blocks, A and B, are placed in contact on a smooth horizontal surface. Block A has a mass of 4.0 kg and block B has a mass of 6.0 kg. A constant horizontal force

F = 50\ \text{N}

is applied to block A in the direction from A towards B, so that both blocks accelerate together.

(a)

Determine the acceleration of the two-block system. [2 marks]

(b)

Determine the magnitude of the contact force that block A exerts on block B. [2 marks]

(c)

The smooth surface is replaced by a rough horizontal surface. The coefficient of kinetic friction between each block and the surface is 0.20. The same force

F = 50\ \text{N}

is applied to block A. (i) Determine the acceleration of the two-block system on the rough surface. [2]
(ii) Determine the contact force between the blocks on the rough surface and evaluate whether it is greater than, equal to, or less than the value found in (b). Justify your answer with reference to Newton's second law applied to block B. [3 marks]

Solutions

30MasterySAQ-SNewton’s laws of motion5 marksPaper 2~8 min

Two blocks, A and B, are placed in contact on a smooth horizontal surface. Block A has mass 2.0 kg and block B has mass 3.0 kg. A horizontal force of 15 N is applied to block A directed toward block B, causing both blocks to accelerate to the right.

(a)

State Newton's third law of motion. [1 mark]

(b)

Calculate the acceleration of the two-block system. [2 marks]

(c)

Determine the magnitude of the contact force that block A exerts on block B. [1 mark]

(d)

Explain why the contact force on block B is less than 15 N. [1 mark]

Solutions

Space, Time, and Motion — Free Physics SL Practice Questions