Chapter Assessment

Mechanics 1

Motion

Chapter Assessment

1. A snail moving across the lawn for her evening constitutional crawl is attracted to a ‘live’ wire. On reaching the wire her speed increases at a constant rate and it doubles from 0.001 ms-1 in ten seconds. She remains at this speed for a further 15 seconds while she remains in contact with the wire. (i) Draw a velocity–time graph to represent this situation when the snail is in

contact with the wire. [4] (ii) Calculate the acceleration. [2] (iii) Calculate the distance travelled during this time. [4]

2. A particle is constrained to move along a straight line through O. It starts initially at D, which is a fixed distance from O in the positive direction and moves at a constant velocity of 4 ms-1 for 15 seconds until it is 100 m from O. It remains 100 m from O for a further 25 seconds, after which it travels in the opposite direction for 20 seconds. The total distance travelled is 180 m. (i) Draw a distance-time graph to represent this situation. [4] (ii) What is the velocity in the final stage of the journey? [2] (iii) How far from O does the particle stop? [1] (iv) Draw a velocity–time graph. [4] (v) What is the final displacement of the particle? [2]

3. A, B and C are three points lying in that order on a straight road with AB = 5 km and BC = 4 km. A man runs from A to B at 20 kmh-1 and then walks from B to C at 8 kmh-1. Find: (i) the total time taken to travel from A to C [3] (ii) the average speed of the man from A to C. [3]

4. A particle travels in a straight line. The motion is modelled by the v-t diagram below. velocity in metres per second time in seconds t v 20 -10 10 0 8765432 1

(i) Calculate the acceleration of the particle in the part of the motion from t = 1 to t = 4. [2] (ii) Calculate the displacement of the particle from its position when t = 0 to its position when t = 6. [4] (iii) Calculate the displacement of the particle from its position when t = 0 to its position when t = 7. [2] (iv) Describe the motion of the particle during the interval 4 ≤ t ≤ 7. [2] Time in seconds Acceleration in ms-2t a -5 5 2 0 7 654321

5. A car is travelling due east along a straight road when it passes a point P. The acceleration of the car during the next 7 seconds is modelled in the acceleration-time graph above, where a ms-2 is the acceleration of the car due east and t seconds is the time after passing the point P. (i) Explain why the speed of the car is greatest when t = 6. [1] The speed of the car when it passes P is 12 ms-1. (ii) Calculate the speed of the car when t = 3. [3] (iii) Show that, when t = 5, the speed of the car is 25 ms-1. [3] (iv) Show that, for 5 ≤ t ≤ 7, the acceleration is given by a = -5t + 30. [2] (v) Explain how the graph may be used to show that the speeds at t = 5 and t = 7 are equal. [2]

Total: 50