v t 2 2t 8. Fig. 7 (i) Write down the velocity of the insect when t 0. (ii) Show that the insect is instantaneously at rest when t 2and when t 4.

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1 1 Fig. 7 is a sketch of part of the velocity-time graph for the motion of an insect walking in a straight line. Its velocity, v ms 1, at time t seconds for the time interval 3 t 5 is given by v ms -1 v t 2 2t. O t seconds A not to scale Fig. 7 (i) Write down the velocity of the insect when t. (ii) Show that the insect is instantaneously at rest when t 2and when t 4. (iii) Determine the velocity of the insect when its acceleration is zero. Write down the coordinates of the point A shown in Fig. 7. [5] (iv) Calculate the distance travelled by the insect from t 1 to t 4. [5] (v) Write down the distance travelled by the insect in the time interval 2 t 4. (vi) How far does the insect walk in the time interval 1 t 5?

2 2 A toy car is travelling in a straight horizontal line. One model of the motion for velocity time graph Fig. 6. velocity in ms 1 v 12 t, where t is the time in seconds, is shown in the 2 4 t time in seconds Fig. 6 (i) Calculate the distance travelled by the car from t to t. (ii) How much less time would the car have taken to travel this distance if it had maintained its initial speed throughout? (iii) What is the acceleration of the car when t 1? From t to t 14, the car travels 5.5 m with a new constant acceleration, a m s 2. (iv) Find a. A second model for the velocity, v m s 1, of the toy car is v 12 t 9 4 t 2 1 t 3, for t. This model agrees with the values for v given in Fig. 6 for t, 2, 4 and 6. [Note that you are not required to verify this.] Use this second model to answer the following questions. (v) Calculate the acceleration of the car when t 1. (vi) Initially the car is at A. Find an expression in terms of t for the displacement of the car from A after the first t seconds of its motion. Hence find the displacement of the car from A when t. [5] (vii) Explain with a reason what this model predicts for the motion of the car between t 2 t 4. and

3 3 A particle travels along a straight line. lls acceleration during the time interval O..; t..; is given by the acceleration-time graph in Fig. l. acceleration a in ms t time in seconds Fig. I (i) Write down the acceleration of the particle when t = 4. Given that the particle starts from rest, find its speed when t = 4. [2) (ii) Write down an expression in terms oft for the acceleration, ams- 2, of the particle in the time interval O o;;; to;;; 4. [l) (iii) Without calculation, state the time at which the speed of the particle is greatest. Give a reason b (iv) Calculate the change in speed of the particle from t = 5 to t =, indicating whether this is an increase or a decrease. [3)

4 4 The speed of a metre runner in m s 1 is measured electronically every 4 seconds. The measurements are plotted as points on the speed-time graph in Fig. 6. The vertical dotted line is drawn through the runner s finishing time. Fig. 6 also illustrates Model P in which the points are joined by straight lines. speed in m s time in s Fig. 6 (i) Use Model P to estimate (A) the distance the runner has gone at the end of 12 seconds, (B) how long the runner took to complete m. [6] A mathematician proposes Model Q in which the runner s speed, v m s 1 at time t s, is given by v = 2 5 t - 1 t 2. (ii) Verify that Model Q gives the correct speed for t =. (iii) Use Model Q to estimate the distance the runner has gone at the end of 12 seconds. [4] (iv) The runner was timed at seconds for the m. Which model places the runner closer to the finishing line at this time? (v) Find the greatest acceleration of the runner according to each model. [4]

5 5 An object C is moving along a vertical straight line. Fig. 1 shows the velocity-time graph for part of 1 its motion. Initially C is moving upwards at 14 m s and after s it is moving downwards at 6 m s 1. v m s t s 5 Fig. 1 C then moves as follows. In the interval t 15, the velocity of C is constant at 6 m s 1 downwards. In the interval 15 t 2, the velocity of C increases uniformly so that C has zero velocity at t = 2. (i) Complete the velocity-time graph for the motion of C in the time interval t 2. (ii) Calculate the acceleration of C in the time interval < t <. (iii) Calculate the displacement of C from t = to t = 2. [4]