Question

Two cars $c_1$, and $c_2$ moving in the same direction on a straight single lane road with velocities $v_1=12m{s}^{-1}$ and $v_2=10m{s}^{-1}$, respectively. When the separation between the two was d = 200 m, $c_2$ started accelerating to avoid collision. What is the minimum acceleration of car $c_2$ so that they do not collide?

Answer 1

$V_1=12m/s{V}_2=10m/s$

Distance between them $d=200m$

Acceleration of $c_2=?$

To avoid collision $c_2$ should retard relative velocity of $c_1$ with respect to

$c_2=\mu =V_1-V_2=12-10=12m/s$

Relative velocity becomes zero for cars to avoid collision so, final velocity $V=0$ (both have same velocity)

Using, $V^2={\mu }^2+2as\Rightarrow 0=(V_1-V_2{)}^2+2a\times 200a=-\frac{(2{)}^2}{2\times 200}a=-\frac{4}{2\times 200}a=-0.01m/s^2$

$-ve$ sign shows retardation.