CAIE M1 2016 November — Question 7

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2016
SessionNovember
TopicSUVAT & Travel Graphs

7 A car starts from rest and moves in a straight line from point \(A\) with constant acceleration \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 10 s . The car then travels at constant speed for 30 s before decelerating uniformly, coming to rest at point \(B\). The distance \(A B\) is 1.5 km .
  1. Find the total distance travelled in the first 40 s of motion. When the car has been moving for 20 s , a motorcycle starts from rest and accelerates uniformly in a straight line from point \(A\) to a speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It then maintains this speed for 30 s before decelerating uniformly to rest at point \(B\). The motorcycle comes to rest at the same time as the car.
  2. Given that the magnitude of the acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) of the motorcycle is three times the magnitude of its deceleration, find the value of \(a\).
  3. Sketch the displacement-time graph for the motion of the car.