Acyclist is going in the positive x-direction at 9m/s. a car initially at rest, accelerates for the first 10 seconds, then it goes with a constant velocity. if the car reaches the cyclist after 15 seconds from the moment the car started moving, find: (a) the acceleration of the car during the first 10 seconds, (b) the velocity of the cyclist with respect to the car when the car reaches the cyclist

1) The car is initially at rest, and it accelerates for the first 10 seconds with acceleration a, so the distance it covers in these first 10 seconds is (in meters)

The velocity the car has reached after these 10 seconds is
(3)
Then the car moves for other 5 seconds with this constant velocity (v=10 a) before reaching the cyclist. During this time, the distance it covers is

So the total distance covered by the car is
(1)

The cyclist is moving at constant speed of , so the distance it covered during the 15 seconds is
(2)

And since the car covered the same distance during this time, we can use (1) and (2) to find the acceleration of the car during the first 10 seconds:


2) The velocity of the car when it reaches the cyclist is given by (3):

The velocity of the cyclist is , therefore the velocity of the car relative to the cyclist is