Question

Two cars $C_1$ and $C_2$ moving in the a same direction on a straight single lane road with velocities $12m/s$ and $10m/s$ respectively. When the separation between the two was $200m,$ $C_2$ started accelerating to avoid a collision. What is the minimum acceleration of car $C_2$ so that they don't collide?

• A. $1cm/s^2$
• B. $4cm/s^2$
• C. $2cm/s^2$
• D. $3cm/s^2$

Answer 1

The correct option is A $1cm/s^2$

The collision is just avoided if relative velocity becomes zero just at the moment the two cars meet each other.
$v_{12}=0when{s}_{12}=200$
$u_{12}=2,{\overline{a}}_{12}=-a$ and $s_{12}=200$

$v_{12}^2-u_{12}^2=2a_{12}{s}_{12}$
$0-2^2=-2\times a\times 200$

$a=\frac{1}{100}m/s^2=0.01m/s^2=1cm/s^2$