Question

Two cars ${\text{C}}_1$ and ${\text{C}}_2$ moving in the same direction on a straight single lane road with velocities $12m/s$ and $10m/s$ respectively. When the separation between the two was $200m$, ${\text{C}}_1$ started decelerating to avoid the collision. What is the minimum retardation of car ${\text{C}}_1$ so that they don't collide?

• A. $1m/s^2$
• B. $1cm/s^2$
• C. $0.1m/s^2$
• D. $0.01cm/s^2$

Answer 1

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



Acceleration of car 1 w.r.t car 2,
$\overrightarrow{a_{12}}=\overrightarrow{a_1}-\overrightarrow{a_2}=\overrightarrow{a_{C_1}}-\overrightarrow{a_{C_2}}=0-a=-a$

$\overrightarrow{u_{12}}=\overrightarrow{u_1}-\overrightarrow{u_2}=12-10=2m/s$

The collision is just avoided if relative velocity becomes zero just at the moment the two cars meet each other.
i.e $v_{12}=0$ when $s_{12}=200$

Now, $v_{12}=0,\overrightarrow{u_{12}}=2,\overrightarrow{a_{12}}=-a$ and $\overrightarrow{s_{12}}=200$
Using 3rd equation of motion,
$v_{12}^2-u_{12}^2=2a{s}_{12}$
$\Rightarrow 0^2-2^2=-2a\times 200$
$\Rightarrow a=\frac{1}{100}=0.01m/s^2=1cm/s^2$

$\therefore$ Minimum retardation needed by car ${\text{C}}_1=1cm/s^2$