Question

A bus travelling at a constant velocity of 72km/he passes a stationary car. After a time lapse of 1/6 minutes, the car accelerates uniformly at 3m/s^2 to reach a speed of 108km/hr and maintains this speed afterwards. Draw the speed-time graph and find when and where the car overtakes the bus.

Answer 1

Velocity of bus, $v_b=72\space km/h=20\space m/s$

Velocity of car, $v_c=108\space km/h=30\space m/s$

Acceleration of car, $a_c=3\space m/s^2$

Acceleration of bus, $a_b=0$

Initial separation of bus and car, $s=20\times10=200\space m$

Velocity of bus with respect to car, $v_{bc}=v_b-v_c=-10\space m/s$

Acceleration of bus with respect to car, $a_{bc}=-3\space m/s^2$

time taken by car to reach bus $=t$

$s=ut+\dfrac{1}{2}at^2$

$-200=-10t+\dfrac{1}{2}(-3)t^2$

$3t^2+20t-200=0$

$t=5.48\space s$