A car is driving along a straight line with a speed v0. At time t = 0 the car is at the origin. At a later instant of time t = t1 the car starts to slow down until it stops at a time t = t2. The acceleration of the car as a function of time is given by

ac = 0, if 0 < t < t1

ac= -c(t-t1), if t1 < t < t2 (1)

where c is a positive constant which has dimensions of acceleration per unit time.

(a) Find vc(t) and xc(t), the x-component of the velocity and the position of the car as a function of time. Express your answer in terms of some or all of the following variables: v0, c, t, t1 and t2.

(b) A bicycle rider is riding at a constant speed of vb and at t = 0 is 17 m behind the car. The cyclist reaches the car when the car just comes to rest. The car is moving with an acceleration

ac= 0, if 0 < t < t1
ac= -c(t-t), if t1 < t < t2 (2)

where its initial component of the velocity is v0 = 12 m/s, t1 = 1 s and c = 6 m/s3.

The car comes to rest at t2. Find the speed of the bicycle to 2 significant figures.