Grade 10 core mathematics – Linear Motion Quiz
1. What is the definition of speed in linear motion?
Speed is a scalar quantity that measures how much distance is covered in a given time interval (distance divided by time). Rate of change of displacement including direction is velocity, change in velocity per time is acceleration, and distance from the starting point is displacement (if signed).
2. Which statement best distinguishes velocity from speed?
Velocity is a vector (it has both magnitude and direction). Speed is a scalar and gives only how fast an object moves without direction.
3. Convert 72 km/h to metres per second.
To convert km/h to m/s multiply by 5/18: 72 × 5/18 = 72/3.6 = 20 m/s.
4. A matatu travels 150 km in 3 hours. What is its average speed?
Average speed = total distance / total time = 150 km / 3 h = 50 km/h.
5. A runner goes 10 km east then 10 km west back to the start. What is the displacement?
Displacement is the net change in position. Returning to the start means net change is zero, so displacement = 0 km.
6. Which best describes uniform motion?
Uniform motion means the object moves with constant speed (and constant direction), so it covers equal distances in equal times along a straight line.
7. A car accelerates uniformly from rest to 20 m/s in 10 s. What is its acceleration?
Acceleration = change in velocity / time = (20 - 0) m/s ÷ 10 s = 2 m/s^2.
8. A stone is dropped from rest and falls with acceleration 2 m/s^2 for 5 s. How far does it fall (use s = ut + 1/2 at^2)?
With u = 0, s = 0 + 1/2 × 2 × 5^2 = 1 × 25 = 25 m.
9. A vehicle starting from rest reaches 30 m/s under constant acceleration of 3 m/s^2. How far did it travel? (Use v^2 = u^2 + 2as.)
Using v^2 = u^2 + 2as with u = 0: s = v^2/(2a) = 30^2/(2×3) = 900/6 = 150 m.
10. A car travels 100 km at 50 km/h and another 100 km at 100 km/h. What is the average speed for the whole trip?
Total distance = 200 km. Time = 100/50 + 100/100 = 2 + 1 = 3 h. Average speed = 200/3 ≈ 66.67 km/h.
11. Two people walk towards each other, one at 4 m/s and the other at 6 m/s. What is their relative speed?
When two objects move towards each other, relative speed = sum of their speeds: 4 + 6 = 10 m/s.
12. On a distance-time graph, what does the slope of the line represent?
Slope on a distance-time graph is rise/run = change in distance / change in time, which is speed.
13. A car travels at 20 m/s for 10 s, then at 10 m/s for 10 s. What is its average speed over the 20 s?
Total distance = 20×10 + 10×10 = 200 + 100 = 300 m. Average speed = 300 m / 20 s = 15 m/s.
14. What term is commonly used to describe negative acceleration (speed decreasing) in everyday language?
Deceleration means a reduction in speed (negative acceleration). Acceleration is the general term, jerk is change of acceleration, and displacement is position change.
15. How long will it take to cover 500 m at a steady speed of 5 m/s?
Time = distance / speed = 500 m ÷ 5 m/s = 100 s.
16. Which equation correctly relates displacement s, initial speed u, time t and constant acceleration a?
For constant acceleration, displacement s = ut + (1/2) a t^2, where u is initial speed, a acceleration and t time.
17. A train speeds up uniformly from 10 m/s to 30 m/s in 20 s. What is its acceleration?
Acceleration = (final - initial) / time = (30 - 10) / 20 = 20/20 = 1 m/s^2.
18. A lorry covers 360 km in 4 hours. What is its speed in metres per second?
Speed = 360/4 = 90 km/h. Convert to m/s: 90 × 5/18 = 90/3.6 = 25 m/s.
19. A car moving at 20 m/s brakes uniformly with acceleration -4 m/s^2. How far does it travel before stopping?
Stopping distance s = v^2/(2|a|) = 20^2 / (2×4) = 400/8 = 50 m.
20. What is the instantaneous speed of an object?
Instantaneous speed is how fast an object is moving at a particular moment; average speed is over a period, and change in velocity is acceleration.
21. A car moves along a straight line in the negative direction. Which sign would its displacement have if we take positive to the right?
If right is positive, motion to the left (negative direction) gives displacement with a negative sign.
22. A small insect crawls 1.5 m at a constant speed of 0.02 m/s. How long does the journey take?
Time = distance / speed = 1.5 ÷ 0.02 = 75 seconds.
23. Two cars 500 m apart move towards each other at 15 m/s and 10 m/s. How long until they meet?
Relative speed = 15 + 10 = 25 m/s. Time = distance / relative speed = 500 / 25 = 20 s.
24. A cyclist covers the first half of a journey at 12 km/h and the second half at 18 km/h (equal distances). What is the average speed for the whole journey?
For equal distances, average speed = 2/(1/v1 + 1/v2) = 2/(1/12 + 1/18) = 2/( (3+2)/36 ) = 72/5 = 14.4 km/h.
25. A vehicle starts at 8 m/s and accelerates uniformly at 2 m/s^2 for 5 s. What is its final speed?
Final speed v = u + at = 8 + (2 × 5) = 8 + 10 = 18 m/s.
26. Which of the following best describes 'speed' in linear motion?
Speed is a scalar: it gives how fast an object moves (distance per unit time) without direction. Velocity is the corresponding vector (includes direction); change in velocity per unit time is acceleration.
27. Convert 72 km/h to metres per second (m/s).
1 km/h = 1000/3600 = 1/3.6 m/s. So 72 km/h = 72 ÷ 3.6 = 20 m/s.
28. On a distance–time graph, what does a horizontal line parallel to the time axis represent?
A horizontal distance–time line means distance does not change as time passes, so the object is not moving and speed is zero.
29. A car travels at a uniform speed of 60 km/h for 2 hours. What distance does it cover?
Distance = speed × time = 60 km/h × 2 h = 120 km.
30. A student travels 30 km in 0.5 hours and then 45 km in 1.0 hour. What is the student's average speed for the whole trip?
Average speed = total distance / total time = (30 + 45) km / (0.5 + 1.0) h = 75 km / 1.5 h = 50 km/h.
31. What is the definition of acceleration in linear motion?
Acceleration measures how velocity changes each second (Δv/Δt). Distance per time is speed; speed in a direction is velocity.
32. A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. What is its final speed?
Use v = u + at. With u = 0, a = 2 m/s², t = 5 s → v = 0 + (2)(5) = 10 m/s.
33. A vehicle starts from rest with constant acceleration 3 m/s² for 4 s. How far does it travel in that time?
Use s = ut + 1/2 at². With u=0, a=3, t=4 → s = 0 + 0.5×3×16 = 24 m.
34. A particle has initial speed 5 m/s, accelerates at 2 m/s² for 10 m. What is its final speed? Use v² = u² + 2as.
v² = 5² + 2×2×10 = 25 + 40 = 65 so v = √65 ≈ 8.062 m/s.
35. On a speed–time graph, the area under the curve between two times represents:
Area under speed (or speed–time) curve over a time interval equals the distance covered during that interval (speed × time integrated).
36. Two cars start 200 km apart and travel towards each other with speeds 40 km/h and 60 km/h. How long until they meet?
Relative speed = 40 + 60 = 100 km/h. Time = distance / relative speed = 200 / 100 = 2 hours.
37. A car moving at 20 m/s decelerates uniformly at 5 m/s² to a stop. How far does it travel before stopping?
Use v² = u² + 2as with v=0: 0 = 20² + 2(−5)s → 0 = 400 −10s → s = 40 m.
38. A ball is thrown straight up with initial speed 15 m/s. Using g = 9.8 m/s², how long does it take to reach its highest point?
Time to top: v = u − g t, with v=0 → t = u/g = 15 / 9.8 ≈ 1.5306 s.
39. A student walks 5 m east, then 3 m west. What is the student's displacement?
Displacement = final position − initial. East 5 then west 3 → net 5 − 3 = 2 m east. Distance travelled would be 8 m.
40. On a distance–time graph, a straight line with constant positive slope indicates:
A straight line means distance increases uniformly with time; the slope (distance/time) is constant, so speed is constant.
41. A cyclist covers 4 km in 15 minutes. What is the average speed in km/h?
15 minutes = 0.25 h. Speed = distance/time = 4 km / 0.25 h = 16 km/h.
42. Convert 18 m/s to km/h.
Multiply by 3.6: 18 × 3.6 = 64.8 km/h.
43. A particle's velocity is −10 m/s. What does the negative sign indicate?
Negative velocity indicates direction opposite to the chosen positive axis. Speed is the magnitude (10 m/s) and cannot be negative.
44. A bus travels 240 km at a steady speed of 80 km/h. How long does the journey take?
Time = distance / speed = 240 km / 80 km/h = 3 hours.
45. What are the SI units of acceleration?
Acceleration is change in velocity (m/s) per second, so units are m/s per s = m/s².
46. What does the gradient of a distance–time graph represent?
Gradient = rise/run = change in distance / change in time, which is speed.
47. Runner A completes 100 m in 12 s and Runner B completes 100 m in 10 s. Who has the greater average speed?
Average speed = distance/time. Runner A: 100/12 ≈ 8.33 m/s; Runner B: 100/10 = 10 m/s. Runner B is faster.
48. An object starting from rest accelerates uniformly at 4 m/s². How long does it take to reach 20 m/s?
Use v = u + at. With u = 0, v = 20, a = 4 → t = v/a = 20/4 = 5 s.
49. A car slows uniformly from 30 m/s to 10 m/s in 5 s. What is its acceleration?
a = (v − u)/t = (10 − 30) / 5 = −20 / 5 = −4 m/s². Negative sign shows deceleration.
50. The position of a particle is given by s(t) = 3t² + 2t (s in metres, t in seconds). What is its velocity at t = 2 s?
Velocity is ds/dt = 6t + 2. At t = 2: v = 6×2 + 2 = 12 + 2 = 14 m/s.