Car A is moving at a constant speed of 10 m/s and passes car B which is at rest. Half a minute later the latter follows with an acceleration of 0.5m/s^2. Determine the distance that the latter has to travel before it overtakes the former.

Answer 1

Start time = 0 when A passes B
(t is measured in seconds)

Xa = distance ravelled by A
Xb = distance travelled by B

Xa = 10 t
Xb = 0.25 (t-30)^2 (t > 30 only)

Solve for when Xa = Xb.

0.25 t^2 -15 t + 225 = 10 t
0.25 t^2 -25t +225 = 0
t^2 -100t + 900 = 0
(t - 90)(t -10) = 0
Only t = 90 seconds satisfies t>30 requirement