Question

Two cars and are travelling in the same direction with velocities $v_1$ and $v_2$ $(v_1$ > $v_2)$. When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a There will be no collision when

• A. $d<\frac{(v_1-v_2{)}^2}{2a}$
• B. $d<\frac{(v_1^2-v_2^2{)}^2}{2a}$
• C. $d>\frac{(v_1-v_2{)}^2}{2a}$
• D. $d>\frac{(v_1^2-v_2^2{)}^2}{2a}$

Answer 1

The correct option is C $d>\frac{(v_1-v_2{)}^2}{2a}$

Initial relative velocity = $v_1-v_2$, Final relative velocity = 0
From $v^2=u^2-2as\Rightarrow 0=(v_1-v_2{)}^2-2\times a\times s$
$\Rightarrow$ $s=\frac{(v_1-v_2{)}^2}{2a}$
If the distance between two cars is 's' then collision will take place. To avoid collision $d>s$ $\therefore$ $d>\frac{(v_1-v_2{)}^2}{2a}$
where d = actual initial distance between two cars.