Question

Two cars are travelling towards each other on a straight road at velocities $15m/s$ and $16m/s$ respectively. When they are $150m$ apart, both the drivers apply the brakes and the cars decelerate at $3m/s^2$ and $4m/s^2$ until they stop. Separation between the cars when they come to rest is :

Answer 1

We know, $v^2=u^2-2as$

Given,

Initial velocity of car 1, $u_1=15m/s$, Acceleration, $a=3m/s^2$

Initial velocity of car 2, $u_2=16m/s$, Acceleration, $a=4m/s^2$

For car 1,

Final Velocity, $v_1=0m/s$

$-{15}^2=-2\left(3\right)\times s$

$\therefore s_1=37.5$ m

For car 2,

Final Velocity, $v_2=0m/s$

$-{16}^2=-2\left(4\right)\times s$

$\therefore s_2=32$ m

Total displacement,

$s_1+s_2=37.5+32=69.5$ m

$\therefore$ separation between them,

$=150-69.5=80.5$ m