Question

Two cars $A$ and $B$ 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. $d < \frac{v_{1}^{2} - v_{2}^{2}}{2a}$
• C. $d > \frac{(v_{1} - v_{2})^{2}}{2a}$
• D. $d > \frac{v_{1}^{2} - v_{2}^{2}}{2a}$

Answer 1

Answer: (C)

$d > \frac{(v_{1} - v_{2})^{2}}{2a}$

Answer 2

Initial relative velocity$= v_{1} - v_{2}$,

Final relative velocity $= 0$

From $v^{2} = u^{2} - 2as$⇒$0 = (v_{1} - v_{2})^{2} - 2 \times a \times s$

⇒ $s = \frac{(v_{1} - v_{2})^{2}}{2a}$

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.