Kinematics

Maths, HSSC-Punjab Second Year. This chapter is split into 33 topics and has 791 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Deriving the equations of motion by integration 22 questions
2. Position of a particle: turning points and returns 24 questions
3. Instantaneous velocity from the position function 26 questions
4. Displacement-time graph: slope and shape 24 questions
5. Time of flight and speed on return 24 questions
6. Displacement-time graph with stages of a journey 26 questions
7. Distance travelled when the velocity changes sign 24 questions
8. Displacement and distance from velocity-time graphs above and below the axis 24 questions
9. Constant-acceleration graph problems 22 questions
10. Units and conversions in kinematics 24 questions
11. Acceleration from position and velocity functions 26 questions
12. Average velocity and average speed 28 questions
13. Variable acceleration: trigonometric, exponential and rational forms 22 questions
14. Combined constant-acceleration problems 26 questions
15. Rectilinear motion: scalars and vectors 22 questions
16. Two stones dropped one second apart 22 questions
17. Velocity-displacement relation 2ax = v² − u² 26 questions
18. Displacement from velocity-time graphs (trapezium and triangle areas) 28 questions
19. Distance covered in a particular second 22 questions
20. Trains and vehicles with speeds in km/h 23 questions
21. Braking and stopping problems 26 questions
22. Sign convention for direction in straight-line motion 21 questions
23. Instantaneous speed and direction of motion 24 questions
24. Acceleration when velocity is given as a function of displacement 22 questions
25. Final velocity v = u + at 26 questions
26. Displacement and distance for out-and-back journeys 22 questions
27. Velocity and position from a given acceleration function 21 questions
28. Free fall from rest 26 questions
29. Displacement x = ut + ½at² 26 questions
30. Vertical upward motion: maximum height 26 questions
31. Velocity-time graph with an unknown initial velocity 22 questions
32. Two bodies meeting under gravity 22 questions
33. Velocity-time graph: slope and area 22 questions

Sample questions: Kinematics

10 sample questions with the correct answer and an explanation. Try to answer each one before reading the explanation.

Q1. A particle moving in the positive direction is brought to rest and then moves in the negative direction under a constant negative acceleration. During the whole motion the acceleration is:

• A. negative throughout(correct answer)
• B. positive after it stops
• C. zero when it stops
• D. changes sign when it stops

Answer: A.The velocity changes from positive to negative through zero, but the acceleration stays the same constant negative value.

Q2. A man walks 180 m east in 4 minutes, then 60 m west in 2 minutes. Taking east as positive, his average velocity (in m/min) is:

• A. 20(correct answer)
• B. 120
• C. −20
• D. 40

Answer: A.Average velocity = total displacement/total time = (180 − 60)/(4 + 2) = 120/6 = 20 m/min (towards the east if positive).

Q3. A man walks 200 m east in 4 minutes, then 80 m west in 1 minute. Taking east as positive, his average velocity (in m/min) is:

• A. 24(correct answer)
• B. 56
• C. −24
• D. 140

Answer: A.Average velocity = total displacement/total time = (200 − 80)/(4 + 1) = 120/5 = 24 m/min (towards the east if positive).

Q4. A man walks 120 m east in 3 minutes, then 40 m west in 2 minutes. Taking east as positive, his average velocity (in m/min) is:

• A. 32
• B. 16(correct answer)
• C. 80
• D. −16

Answer: B.Average velocity = total displacement/total time = (120 − 40)/(3 + 2) = 80/5 = 16 m/min (towards the east if positive).

Q5. A man walks 100 m east in 2 minutes, then 60 m west in 1 minute. Taking east as positive, his average velocity (in m/min) is:

• A. 80
• B. 53.33
• C. 13.33(correct answer)
• D. −13.33

Answer: C.Average velocity = total displacement/total time = (100 − 60)/(2 + 1) = 40/3 = 13.33 m/min (towards the east if positive).

Q6. A man walks 50 m east in 2 minutes, then 70 m west in 3 minutes. Taking east as positive, his average velocity (in m/min) is:

• A. 24
• B. 60
• C. 4
• D. −4(correct answer)

Answer: D.Average velocity = total displacement/total time = (50 − 70)/(2 + 3) = −20/5 = −4 m/min (towards the east if positive).

Q7. A man walks 300 m east in 5 minutes, then 120 m west in 5 minutes. Taking east as positive, his average velocity (in m/min) is:

• A. 18(correct answer)
• B. −18
• C. 42
• D. 210

Answer: A.Average velocity = total displacement/total time = (300 − 120)/(5 + 5) = 180/10 = 18 m/min (towards the east if positive).

Q8. A bus travels 3 km along a straight highway to a terminal and then returns along the same highway to the starting stop after 1 h. The bus's average velocity for the round trip (km/h) is:

• A. −3
• B. 0(correct answer)
• C. 6
• D. 3

Answer: B.The net displacement is zero (the starting point is regained), so the average velocity is 0/1 = 0 km/h even though the average speed was 6 km/h.

Q9. A delivery van drives 6 km straight out from a depot and returns to the same depot, the round trip lasting 2 h. Its average velocity over the round trip is (km/h):

• A. −3
• B. 3
• C. 0(correct answer)
• D. 6

Answer: C.The net displacement is zero (the starting point is regained), so the average velocity is 0/2 = 0 km/h even though the average speed was 6 km/h.

Q10. A cyclist rides 4 km along a straight road and rides back to the start, taking 1.5 h in all. Her average velocity for the whole journey (in km/h) is:

• A. 0(correct answer)
• B. 2.67
• C. 5.33
• D. −2.67

Answer: A.The net displacement is zero (the starting point is regained), so the average velocity is 0/1.5 = 0 km/h even though the average speed was 5.33 km/h.