Senior 1 practice book · Unit 2 of 9

Uniform Rectilinear Motion

50 questions that complete the Senior 1 quiz for this unit: 30 core and 20 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Average speed is the average of the speeds: (v₁ + v₂) ÷ 2.Average speed = total distance ÷ total time. If the two speeds last for different times, simply averaging them gives the wrong answer.
A distance–time graph shows the path or the hill the object travels along.A distance–time graph shows how far the object is from the start at each moment. A rising line does not mean the object goes uphill; it means it moves away from the start.
Constant speed means constant velocity.Velocity includes direction. A moto going round a roundabout at a steady 30 km/h has constant speed but its velocity keeps changing because its direction changes.
Zero velocity means zero acceleration.Acceleration is the rate of change of velocity. A ball thrown upwards is momentarily at rest at the top but its velocity is still changing, so it is still accelerating.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Rest and motion relative to a reference point; types of motion (rectilinear, circular, rotational, oscillatory, random)
Distance and displacement
Speed and average speed
Velocity and uniform rectilinear motion
Converting speeds between km/h and m/s
Distance–time graphs
Acceleration and deceleration: a = (v − u)/t
Speed–time (velocity–time) graphs: gradient and area
Ticker-tape timer: dot spacing, time intervals and speed
Relative motion: speed of one body relative to another
Measuring speed in practice: planning, timing and reaction time
Displacement–time graphs with return journeys (negative velocity)
Road safety: reaction time, thinking, braking and stopping distances

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 20 harder ones are marked ★ Challenge.

1True or false
Two cars moving side by side at the same velocity are at rest relative to each other.
Show answer
Answer: True
Their relative velocity is zero, so each driver sees the other car staying in the same place.
Common mistakeLearners think a moving car can never be 'at rest', but rest and motion depend on the reference point.
2True or false · ★ Challenge
The same object can be at rest and moving at the same time, depending on the reference point chosen.
Show answer
Answer: True
A sleeping passenger in a moving bus is at rest relative to the bus but moving relative to the road.
Common mistakeThinking motion is absolute ignores that we always describe motion relative to something.
3True or false
If two runners finish a race in the same time, they must have had the same speed at every instant.
Show answer
Answer: False
They had the same average speed, but one may have started fast and slowed down while the other did the opposite.
Common mistakeEqual average speed does not mean equal speed at every moment.
4Multiple choice · ★ Challenge
Which change increases a moto rider's thinking distance but not the braking distance?
1. AThe brake pads are badly worn
2. BThe road is wet and very muddy
3. CThe rider is tired or on a phone
4. DThe tyres have been worn smooth
Show answer
Answer: C. The rider is tired or on a phone
Tiredness and distraction make the reaction time longer, so the moto travels further before the brakes go on.
Common mistakeWet roads and worn tyres are dangerous too, but they affect the braking distance, not the thinking distance.
5Fill in the blank
Stopping distance = thinking distance + ______ distance.
Show answer
Answer: braking
The car first travels during the reaction time (thinking distance), then while the brakes act (braking distance).
Common mistakeLearners forget the thinking distance and think the car starts slowing the moment the danger appears.
6Fill in the blank
A change of velocity in m/s divided by a time in s gives an acceleration in ______.
Show answer
Answer: m/s² (metres per second squared)
Acceleration is change in velocity (m/s) per second, so its unit is m/s².
Common mistakeWriting m/s gives the unit of speed, not of acceleration.
7Fill in the blank · ★ Challenge
Taking forwards as positive, a toy car moves 50 m forwards and then 80 m backwards. Its displacement is ______ m.
Show answer
Answer: −30
Displacement = +50 + (−80) = −30 m, i.e. 30 m behind the starting point.
Common mistakeWriting 130 m adds the distances; displacement must take the directions into account.
8Fill in the blank
The short delay between seeing an event and pressing the stopwatch button is called ______ time.
Show answer
Answer: reaction
Human reaction time is about 0.2 s and causes errors in hand timing.
Common mistakeSome learners call it 'zero error'; zero error belongs to the instrument, reaction time belongs to the person.
9Multiple choice
Which is an example of rotational motion?
1. AA bicycle wheel spinning on its axle
2. BA child going to and fro on a swing
3. CA moto riding along a straight road
4. DDust particles moving about in the air
Show answer
Answer: A. A bicycle wheel spinning on its axle
In rotation the body spins about an axis through itself, like a wheel on its axle.
Common mistakeA swing is tempting, but it moves to and fro about a fixed point: that is oscillatory motion.
10Multiple choice · ★ Challenge
Four vehicles on the Kigali–Rwamagana road are timed. Which one is moving fastest?
1. AA car doing 1.5 km/min
2. BA bus doing 20 m/s
3. CA lorry doing 60 km/h
4. DA moto doing 1 km in 100 s
Show answer
Answer: A. A car doing 1.5 km/min
1.5 km/min = 1500 ÷ 60 = 25 m/s; 60 km/h = 16.7 m/s; 1 km in 100 s = 10 m/s; so the car at 1.5 km/min is fastest.
Common mistakeChoosing the lorry because 60 is the biggest number forgets to convert all the speeds to the same unit.
11True or false
A ticker timer connected to a 50 Hz supply prints 50 dots every second, whatever the speed of the tape.
Show answer
Answer: True
The timer strikes at a fixed rate; the speed of the tape only changes how far apart the dots are.
Common mistakeLearners think a faster tape gets more dots per second; it gets the same number, spread further apart.
12Multiple choice · ★ Challenge
Which set of readings for a trolley shows uniform velocity? (t = 0, 2, 4, 6 s in each case)
1. Ad = 0, 2, 8, 18 m
2. Bd = 0, 6, 12, 18 m
3. Cd = 0, 6, 10, 12 m
4. Dd = 0, 6, 6, 18 m
Show answer
Answer: B. d = 0, 6, 12, 18 m
0, 6, 12, 18 m: the trolley covers 6 m in every 2 s, so its velocity is a steady 3 m/s.
Common mistake0, 2, 8, 18 m also ends at 18 m, but the gaps grow (2, 6, 10 m), which shows acceleration.
13Multiple choice
A passenger sits still in a moving bus. Which statement is correct?
1. AShe is moving relative to the driver but at rest relative to a roadside tree
2. BShe is at rest relative to both the driver and a tree beside the road
3. CShe is at rest relative to the driver but moving relative to a roadside tree
4. DShe is moving relative to both the driver and a tree beside the road
Show answer
Answer: C. She is at rest relative to the driver but moving relative to a roadside tree
Motion depends on the reference point: she keeps the same position relative to the driver, but changes position relative to the tree.
Common mistakeLearners think 'moving' and 'at rest' are fixed facts, but they always depend on what you compare the object with.
14True or false · ★ Challenge
A displacement–time graph can go below the time axis if the object moves to the other side of its starting point.
Show answer
Answer: True
Displacement has direction, so positions on the opposite side of the start are negative.
Common mistakeLearners think the graph cannot go below zero because a distance cannot be negative, but displacement can.
15Fill in the blank
To change a speed in m/s into km/h, multiply it by ______.
Show answer
Answer: 3.6
1 m/s = 3600 m per hour = 3.6 km/h.
Common mistakeLearners often divide by 3.6 here; that is the step for km/h to m/s.
16Multiple choice
To measure a classmate's running speed on the school field, you need:
1. AA stopwatch only
2. BA metre rule and a beam balance
3. CA thermometer and a measuring tape
4. DA measuring tape and a stopwatch
Show answer
Answer: D. A measuring tape and a stopwatch
Speed = distance ÷ time, so you must measure a distance (tape) and a time (stopwatch).
Common mistakeA stopwatch alone gives only the time; without the distance, speed cannot be found.
17Multiple choice · ★ Challenge
A goat tied to a peg walks once round a circle of radius 3 m and stops where it started. What are the distance travelled and its displacement? (π = 3.14)
1. A0 m and 18.8 m
2. B9.4 m and 6 m
3. C18.8 m and 0 m
4. D28.3 m and 0 m
Show answer
Answer: C. 18.8 m and 0 m
Distance = 2πr = 2 × 3.14 × 3 = 18.8 m; it ends where it started, so displacement = 0 m.
Common mistake28.3 m comes from πr² (the area of the circle) instead of the circumference 2πr.
18Multiple choice
Part of a ticker tape shows several dots printed on top of one another at the same place. What does this show about the trolley?
1. AIt was moving at a high speed
2. BIt was speeding up steadily
3. CThe timer had stopped working
4. DIt was at rest for a short time
Show answer
Answer: D. It was at rest for a short time
If the tape does not move, every dot lands on the same spot, so the trolley was not moving.
Common mistakeChoosing 'high speed' reverses the idea: fast motion spreads the dots far apart.
19Multiple choice · ★ Challenge
Near a school the speed limit is 30 km/h. A car is timed covering 50 m in 5 s. Is it keeping to the limit?
1. ANo, it is moving at 36 km/h
2. BYes, it is moving at 10 km/h
3. CYes, it is moving at 2.8 km/h
4. DNo, it is moving at 250 km/h
Show answer
Answer: A. No, it is moving at 36 km/h
v = 50 ÷ 5 = 10 m/s = 10 × 3.6 = 36 km/h, which is above 30 km/h.
Common mistake'Yes, 10 km/h' forgets that 10 is in m/s; it must be converted to km/h before comparing with the limit.
20Multiple choice
A moto rides round a roundabout at a steady 30 km/h. Which statement is correct?
1. AIts velocity is constant but its speed changes
2. BIts speed is constant but its velocity changes
3. CBoth its speed and its velocity are constant
4. DIts speed and its velocity both keep changing
Show answer
Answer: B. Its speed is constant but its velocity changes
The size of the speed stays 30 km/h, but the direction changes all the time, so the velocity changes.
Common mistake'Both constant' is tempting because the speedometer does not move, but velocity also depends on direction.
21Multiple choice
A ticker timer makes 50 dots every second. What is the time between two neighbouring dots?
1. A0.02 s
2. B50 s
3. C0.2 s
4. D0.5 s
Show answer
Answer: A. 0.02 s
Time between dots = 1 ÷ 50 = 0.02 s.
Common mistake0.2 s comes from a slip in the decimal place; 1 ÷ 50 = 0.02, not 0.2.
22Multiple choice · ★ Challenge
On the same distance–time graph, the straight lines for two cyclists cross. What does the crossing point show?
1. AThey are moving at the same speed at that moment
2. BBoth of the cyclists have stopped at that moment
3. CThey are at the same place at the same moment
4. DBoth of the cyclists are speeding up at that time
Show answer
Answer: C. They are at the same place at the same moment
Each point on a distance–time graph gives a position at a time, so where the lines cross they are at the same place at the same time.
Common mistakeLearners think crossing lines mean equal speeds, but speed is shown by the slope, not by where lines meet.
23Multiple choice
A passenger walks forwards at 1 m/s along the aisle of a train moving at 20 m/s. What is her speed relative to the ground?
1. A19 m/s
2. B21 m/s
3. C20 m/s
4. D1 m/s
Show answer
Answer: B. 21 m/s
She moves in the same direction as the train, so her speed relative to the ground = 20 + 1 = 21 m/s.
Common mistake19 m/s subtracts the speeds, which would be right only if she walked towards the back of the train.
24Multiple choice
Two buses travel in the same direction on a straight road at 60 km/h and 45 km/h. What is the speed of the faster bus relative to the slower one?
1. A105 km/h
2. B15 km/h
3. C52.5 km/h
4. D0 km/h
Show answer
Answer: B. 15 km/h
Same direction: relative speed = 60 − 45 = 15 km/h.
Common mistake105 km/h adds the speeds, which is only correct when the buses move towards each other.
25Multiple choice · ★ Challenge
On the displacement–time graph of a moving object, a straight line slopes DOWN towards the time axis. What does this show about the object?
1. AIt is slowing down steadily until it comes to a stop
2. BIt is moving away from its start faster and faster
3. CIt is coming back to its start at a steady velocity
4. DIt is at rest at a fixed position away from the start
Show answer
Answer: C. It is coming back to its start at a steady velocity
A falling displacement means the object is getting closer to the start; a straight line means its velocity is constant (and negative).
Common mistakeLearners read a downward slope as 'slowing down', but that would be a curve getting flatter, not a straight falling line.
26Multiple choice
A driver's reaction time is 0.7 s and the car moves at 20 m/s. What is the thinking distance?
1. A28.6 m
2. B14.0 m
3. C20.7 m
4. D2.9 m
Show answer
Answer: B. 14.0 m
Thinking distance = speed × reaction time = 20 × 0.7 = 14 m.
Common mistake28.6 m comes from dividing 20 by 0.7; distance = speed × time.
27Multiple choice · ★ Challenge
A student times a toy car over 10 m and records 2.0 s, but she started the stopwatch 0.2 s late because of her reaction time. What effect does this have on her calculated speed?
1. AIt is too large, because the recorded time is too short
2. BIt is too small, because the recorded time is too short
3. CIt is correct, because reaction time always cancels out
4. DIt is too large, because the distance used is too long
Show answer
Answer: A. It is too large, because the recorded time is too short
Starting late makes the recorded time shorter than the real time, so distance ÷ time gives a speed that is too large.
Common mistakeChoosing 'too small' forgets that dividing by a smaller time gives a bigger answer.
28True or false
A line on a distance–time graph that curves upwards, getting steeper, shows that the object is speeding up.
Show answer
Answer: True
The slope gives the speed, so an increasing slope means increasing speed.
Common mistakeLearners read a rising line as 'going uphill'; the shape shows how speed changes, not the shape of the road.
29Multiple choice · ★ Challenge
A minibus brakes steadily from 15 m/s to rest in 6 s. Using the area under its speed–time graph, how far does it travel while braking?
1. A90 m
2. B2.5 m
3. C45 m
4. D21 m
Show answer
Answer: C. 45 m
The area is a triangle: ½ × 6 × 15 = 45 m.
Common mistake90 m comes from speed × time (a rectangle) and forgets the ½ for a triangle.
30Multiple choice
Convert a speed of 15 m/s to km/h.
1. A4.2 km/h
2. B15 km/h
3. C900 km/h
4. D54 km/h
Show answer
Answer: D. 54 km/h
Multiply by 3.6: 15 × 3.6 = 54 km/h.
Common mistake4.2 km/h comes from dividing by 3.6; going from m/s to km/h the number must get bigger.
31True or false
The slope of the line on a velocity–time graph tells you the acceleration of the object.
Show answer
Answer: True
Slope = change in velocity ÷ time = acceleration.
Common mistakeLearners mix this up with a distance–time graph, whose slope is the speed.
32Multiple choice · ★ Challenge
A ball rolls from rest down a slope with a steady acceleration of 1.5 m/s². What is its speed after 4 s?
1. A2.7 m/s
2. B0.38 m/s
3. C6 m/s
4. D5.5 m/s
Show answer
Answer: C. 6 m/s
v = u + at = 0 + 1.5 × 4 = 6 m/s.
Common mistake0.38 m/s comes from dividing 1.5 by 4; the speed gained is acceleration × time.
33Short answer
Two buses each travel at 60 km/h, one north to Musanze and the other south to Huye. Are their speeds equal? Are their velocities equal? Explain.
Show answer
Model answer: Their speeds are equal (both 60 km/h). Their velocities are not equal because velocity includes direction: one is 60 km/h north, the other 60 km/h south.
Common mistakeLearners treat speed and velocity as the same word; two velocities are equal only if size AND direction are the same.
34Multiple choice
A bus leaves Kigali at 07:00 and reaches Huye, about 130 km away, at 09:30. What is its average speed?
1. A56.5 km/h
2. B65 km/h
3. C43.3 km/h
4. D52 km/h
Show answer
Answer: D. 52 km/h
Time = 2 h 30 min = 2.5 h, so average speed = 130 ÷ 2.5 = 52 km/h.
Common mistake56.5 km/h comes from writing 2 h 30 min as 2.3 h; 30 minutes is half an hour, 0.5 h.
35Short answer · ★ Challenge
How long does a car accelerating steadily at 2.5 m/s² take to go from rest to 90 km/h?
Show answer
Model answer: 90 km/h = 90 ÷ 3.6 = 25 m/s. t = (v − u)/a = (25 − 0) ÷ 2.5 = 10 s.
Common mistakeUsing 90 directly gives 36 s; km/h must be changed to m/s because the acceleration is in m/s².
36Short answer
A bus's average speed for a trip is 40 km/h. Does this mean its speedometer showed 40 km/h all the way? Explain.
Show answer
Model answer: No. The bus went faster on open road and slower or stopped at bus stops and junctions. Average speed is total distance ÷ total time; the speedometer shows the speed at each instant.
Common mistakeLearners confuse average speed with instantaneous speed; an average says nothing about the speed at a particular moment.
37Short answer · ★ Challenge
A moto at 15 m/s is 300 m behind a lorry moving at 10 m/s in the same direction. How long does the moto take to catch up with the lorry?
Show answer
Model answer: Relative speed = 15 − 10 = 5 m/s. Time = 300 ÷ 5 = 60 s.
Common mistakeUsing 15 + 10 = 25 m/s (giving 12 s) treats them as moving towards each other.
38Short answer
A sprinter covers 100 m in 10 s. A moto rides at 40 km/h. Which is faster? Show your working.
Show answer
Model answer: Sprinter: 100 ÷ 10 = 10 m/s = 10 × 3.6 = 36 km/h. The moto at 40 km/h is faster.
Common mistakeComparing 10 with 40 directly is wrong because they are in different units.
39Short answer · ★ Challenge
Plan an experiment to measure the average speed of a trolley rolling down a ramp. State what you measure, the instruments, and two ways to make the result more reliable.
Show answer
Model answer: Mark start and finish lines and measure the distance between them with a metre rule. Release the trolley from rest at the start and time it to the finish with a stopwatch. Speed = distance ÷ time. Repeat several times and take the average time; use a longer ramp so that the time is larger compared with reaction time (or use light gates).
Common mistakeLearners forget to repeat the timing; a single reading includes a large reaction-time error.
40Multiple choice
On a speed–time graph, the area under the line gives the:
1. ADistance covered
2. BAcceleration
3. CAverage speed
4. DTime for the journey
Show answer
Answer: A. Distance covered
Area = speed × time = distance.
Common mistakeChoosing acceleration mixes up area and gradient; the gradient (slope) gives acceleration.
41Multiple choice
A car is parked 50 m from a junction. What does its distance–time graph (distance measured from the junction) look like?
1. AA straight line through the origin
2. BA vertical line at 50 m
3. CA horizontal line along the time axis
4. DA horizontal line at 50 m
Show answer
Answer: D. A horizontal line at 50 m
The distance stays 50 m at all times, so the graph is a horizontal line at 50 m.
Common mistakeChoosing the time axis forgets that the car is not at the junction; at rest means a flat line at its own position.
42Short answer · ★ Challenge
A car moves at 15 m/s. The driver's reaction time is 0.6 s, and the car then brakes steadily to rest in 3 s. Calculate the thinking distance, the braking distance and the stopping distance.
Show answer
Model answer: Thinking distance = 15 × 0.6 = 9 m. Braking distance = ½ × 15 × 3 = 22.5 m. Stopping distance = 9 + 22.5 = 31.5 m.
Common mistakeLearners use 15 × 3 = 45 m for braking, forgetting that the speed falls steadily, so the average speed is only 7.5 m/s.
43Multiple choice
A runner's average speed over 1500 m is 5 m/s. How long does the race take?
1. A5 min
2. B300 min
3. C7500 min
4. D50 min
Show answer
Answer: A. 5 min
t = d ÷ v = 1500 ÷ 5 = 300 s = 300 ÷ 60 = 5 min.
Common mistake300 min forgets that the time from d ÷ v is in seconds, not minutes.
44Short answer · ★ Challenge
A tape from a 50 Hz ticker timer is cut into strips of 5 dot-spaces each. The strips are 1.5 cm, 3.0 cm, 4.5 cm and 6.0 cm long. What type of motion does this show? Find the average speed during the first strip.
Show answer
Model answer: Each strip takes 5 × 0.02 = 0.1 s. The lengths increase by the same amount (1.5 cm) each time, so the trolley has uniform acceleration. Speed in strip 1 = 1.5 cm ÷ 0.1 s = 15 cm/s = 0.15 m/s.
Common mistakeA common mistake is to take each strip as 1 s; 5 spaces at 0.02 s each is only 0.1 s.
45Multiple choice
Leaving a stage, a moto taxi's speed rises from 4 m/s to 16 m/s over 6 s. Calculate the acceleration of the moto.
1. A3.3 m/s²
2. B2 m/s²
3. C2.7 m/s²
4. D72 m/s²
Show answer
Answer: B. 2 m/s²
a = (v − u)/t = (16 − 4) ÷ 6 = 12 ÷ 6 = 2 m/s².
Common mistake3.3 m/s² comes from adding the speeds (20 ÷ 6); acceleration uses the change in speed.
46Short answer
A boy walks from home 500 m east to the market and then 200 m back west to a shop. Find the distance he walks and his displacement from home.
Show answer
Model answer: Distance = 500 + 200 = 700 m. Displacement = 500 − 200 = 300 m east of home.
Common mistakeLearners often give 700 m for both; displacement is measured in a straight line from start to finish and needs a direction.
47Short answer · ★ Challenge
A trolley's speed rises steadily from 0 to 3 m/s in 2 s, stays at 3 m/s for 4 s, then falls steadily to 0 in 3 s. Find its acceleration in the first 2 s and the total distance travelled.
Show answer
Model answer: a = 3 ÷ 2 = 1.5 m/s². Distance = ½ × 2 × 3 + 4 × 3 + ½ × 3 × 3 = 3 + 12 + 4.5 = 19.5 m.
Common mistakeLearners often forget the ½ in the triangle areas, getting 6 + 12 + 9 = 27 m.
48Multiple choice
A displacement–time table for a canoe is: t = 0, 10, 20, 30 s; x = 0, 50, 50, 20 m. What is its velocity between 20 s and 30 s?
1. A+3 m/s (moving away from the start)
2. B+0.67 m/s (moving away from the start)
3. C−2 m/s (moving back towards the start)
4. D−3 m/s (moving back towards the start)
Show answer
Answer: D. −3 m/s (moving back towards the start)
v = (20 − 50) ÷ (30 − 20) = −30 ÷ 10 = −3 m/s.
Common mistake+0.67 m/s comes from 20 ÷ 30, using the readings instead of the changes.
49Short answer
A cyclist's distance–time graph has two straight sections: from (0 s, 0 m) to (5 s, 20 m), then from (5 s, 20 m) to (15 s, 40 m). Find her speed in each section and say which section is faster.
Show answer
Model answer: Section 1: 20 ÷ 5 = 4 m/s. Section 2: (40 − 20) ÷ (15 − 5) = 20 ÷ 10 = 2 m/s. The first section is faster (steeper line).
Common mistakeA common error is to divide 40 by 15 for the second section, using the readings instead of the changes in distance and time.
50Short answer · ★ Challenge
A girl walks from home to a shop 300 m away in 200 s, waits in the shop for 100 s, then walks home in 150 s. Describe her displacement–time graph and find her velocity on the way home.
Show answer
Model answer: The graph rises in a straight line from 0 to 300 m between 0 and 200 s, is horizontal at 300 m from 200 s to 300 s, then falls in a straight line back to 0 m at 450 s. Velocity home = −300 ÷ 150 = −2 m/s, i.e. 2 m/s towards home.
Common mistakeLearners draw the return trip as a rising line because she is still walking; displacement from home decreases on the way back.