Question

Two cars A and B are travelling in the same direction with velocities VA and VB(VA>VB). When car A is at a distance s ahead of car B, the driver of car A applies the brakes producing a uniform retardation a; there will be no collision when

• A. s < (VA - VB)^2 / 2a
• B. s < (VA^2 - VB^2) / 2a
• C. s > (VA - VB)^2 / 2a
• D. s > (VA^2 - VB^2) / 2a

Answer 1

Answer: (C)

s > (VA - VB)^2 / 2a

Answer 2

Initial relative velocity = $V_A - V_B$.

Final relative velocity = 0.

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

⇒ $s = \frac{(V_A - V_B)^{2}}{2a}$

If the distance between two cars is 's' then collision will take place. To avoid collision $d > s$ ∴ $d > \frac{(V_A - V_B)^{2}}{2a}$

where $d =$ actual initial distance between two cars.