Linear Motion

14 Grade 10 Core Mathematics questions on Linear Motion, with worked marking schemes. 14 questions are available on this topic in full.

Question 1
1 mark
For a body in motion, the area between a velocity–time graph and the time axis represents
A. the distance travelled by the body
B. the rate of change of acceleration of the body
C. the average velocity of the body
D. the acceleration of the body
(1 mark)
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Question 2
3 marks
A driver says that because he drove from one town to another at an average speed of 40 km/h and returned along the same road at an average speed of 60 km/h, his average speed for the whole journey is 50 km/h. Explain why the driver is not correct.
(3 marks)
Marking scheme
1. Average speed is total distance divided by total time, not the mean of the two speeds — 1 mark. 2. The two speeds cover equal distances but take unequal times; more time is spent on the slower outward trip — 1 mark. 3. Hence the true average speed is less than 50 km/h (it works out as 48 km/h) — 1 mark.
Question 3
5 marks
A matatu starts from rest at a stage and accelerates uniformly at $2 m / s^{2}$ for 10 seconds. It then travels at the velocity reached for a further 20 seconds. Calculate the total distance covered in the 30 seconds.
(5 marks)
Marking scheme
1. First stage: s = ut + $\frac{1}{2}$ at² with u = 0 — 1 mark for formula. 2. s₁ = $\frac{1}{2}$ × $2 \times 1 0^{2} = 100 m$ — 1 mark. 3. Velocity reached: v = u + at = $0 + 2 \times 10 = 20 m / s$ — 1 mark. 4. Second stage: s₂ = $20 \times 20 = 400 m$ — 1 mark. 5. Total distance = 100 + 400 = 500 m — 1 mark.
Question 4
1 mark
A cyclist and a runner start together from a shopping centre and move along a straight road in opposite directions. The cyclist moves at 18 km/h and the runner at 6 km/h. The distance between them after 40 minutes is
A. 16 km
B. 24 km
C. 9.6 km
D. 8 km
(1 mark)
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Question 5
1 mark
A train approaching a station slows down uniformly from 30 m/s until it comes to rest after 12 seconds. The distance it covers while slowing down is
A. 90 m
B. 180 m
C. 360 m
D. 2.5 m
(1 mark)
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Question 6
3 marks
Distinguish between distance and displacement, using the example of an athlete who runs exactly one complete lap of a 400 m school track.
(3 marks)
Marking scheme
1. Distance is the total length of the path covered and is a scalar (magnitude only) — 1 mark. 2. Displacement is the change in position measured in a straight line from start to finish, in a stated direction, and is a vector — 1 mark. 3. For one complete lap: distance = 400 m, but displacement = 0 because the athlete finishes at the starting point — 1 mark.
Question 7
1 mark
A bus pulling out of a stage increases its velocity uniformly from 5 m/s to 25 m/s in 8 seconds. Its acceleration is
A. $20 m / s^{2}$
B. $2.5 m / s^{2}$
C. $0.4 m / s^{2}$
D. $3.125 m / s^{2}$
(1 mark)
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Question 8
4 marks
A bus leaves a town travelling along a straight highway at a steady 60 km/h. Two hours later a car leaves the same town along the same road at a steady 90 km/h. Calculate the time the car takes to catch up with the bus.
(4 marks)
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Question 9
1 mark
A lorry carrying sugarcane covers 160 km from a factory to a depot in 2 hours 30 minutes. Its average speed for the journey is
A. 53.3 km/h
B. 64 km/h
C. 80 km/h
D. 6.4 km/h
(1 mark)
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Question 10
1 mark
Which one of the following statements about speed and velocity is correct?
A. A body moving with constant speed must also be moving with constant velocity.
B. Velocity is the speed of a body together with the direction of its motion.
C. Velocity is measured in metres while speed is measured in metres per second.
D. Speed is a vector quantity while velocity is a scalar quantity.
(1 mark)
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Question 11
1 mark
A matatu travels along a highway at a steady 72 km/h. This speed expressed in metres per second is
A. 1 200 m/s
B. 259.2 m/s
C. 2 m/s
D. 20 m/s
(1 mark)
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Question 12
4 marks
A lorry carrying tea travels 90 km in 1 hour 30 minutes, stops at a weighbridge for 30 minutes, then travels a further 60 km in 1 hour.
(a) State the total distance covered.
(b) State the total time taken.
(c) Calculate the average speed for the whole journey.
(4 marks)
Marking scheme
(a) 1. Total distance = 90 + 60 = 150 km — 1 mark. (b) 2. Total time = 1 h 30 min + 30 min + 1 h = 3 hours (the stop must be included) — 1 mark. (c) 3. Average speed = total distance ÷ total time — 1 mark for method. 4. = $150 \div 3 = 50$ km/h — 1 mark.
Question 13
3 marks
(a) State what the gradient of a distance–time graph represents.
(b) Describe the motion of a body whose distance–time graph is a horizontal straight line.
(3 marks)
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Question 14
3 marks
A cyclist riding along a straight road passes a shop at 4 m/s and then accelerates uniformly at $1.5 m / s^{2}$ for 12 seconds. Calculate his velocity at the end of the 12 seconds.
(3 marks)
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Linear Motion

Question 1

Question 2

Question 3

Question 4

Question 5

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Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14