Question

Two cars $A$ and $B$ are travelling in the same direction with velocities $v_A$ and $v_B(v_A>v_B)$. When the car $A$ is at a distance $d$ behind the car $B$ the driver of the car $A$ applies brakes producing a uniform retardation $a$. There will be no collision when

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

Answer 1

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

Initial relative velocity $v_A-v_B$, is reduced to $0$ in distance $d^{\prime }(<d)$ with retardation $a$.
$\therefore 0^2-{(v_A-v_B)}^2=2a{d}^{\prime }$
$\therefore d^{\prime }=\frac{{(v_A-v_B)}^2}{2a}$
$\therefore d>\frac{{(v_A-v_B)}^2}{2a}$