Worksheet Chapter 8: Kinematics of Linear Motion

1. Fill in the blank: The rate of change of velocity with respect to time is called ________.

2. A toy car moves along a straight track such that its acceleration is a = 2t - 6 ms⁻². Given that its initial velocity is 5 ms⁻¹ and its displacement at t = 0 is 0 m. (a) Express velocity v in terms of t. (b) Express displacement s in terms of t. (c) Find the displacement of the car when it is at rest.

3. A particle moves along a straight line from a fixed point O with acceleration a = 6t - 18 ms⁻². The initial velocity of the particle is 15 ms⁻¹. (a) Find the expression for velocity v in terms of t. (b) Determine the time interval(s) during which the particle is decelerating. (c) Calculate the displacement of the particle when its acceleration is zero.

4. A particle moves along a straight line with displacement s = t³ - 9t² + 24t meters from fixed point O at time t seconds. Find its initial position.

5. Which of the following functions gives acceleration a if displacement is s = 2t³ - 4t² + 5?

6. State whether the statement is True or False: 'If an object is at rest, its acceleration must be zero.'

7. An object moves along a straight line from a fixed point O with velocity function v = 6t - t² ms⁻¹. (a) Find the time t when velocity is maximum. (b) Calculate the maximum velocity.

8. A particle moves along a straight line passing through a fixed point O with velocity v = 3t² - 12t + 9 ms⁻¹. Find: (a) The values of t when the particle is instantaneously at rest. (b) The acceleration of the particle at t = 3 seconds.

9. A particle moves in a straight line from origin O with velocity v = 12 - 4t ms⁻¹. Calculate the total distance traveled by the particle in the first 5 seconds.

10. A bullet is fired vertically upwards. Its height h meters after t seconds is given by h = 40t - 5t². (a) Find the maximum height reached by the bullet. (b) Find the time taken for the bullet to return to the ground.