JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Kinematics

Two cars are travelling towards each other at speed of

20 m s^{- 1}

each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of

2 m s^{- 2}

. The distance between them when they come to rest is :

(A)200 m
(B)50 m
(C)100 m✓ Correct
(D)25 m

Answer: (C)

Solution

Work in the frame of car A: relative speed of approach

u_{B A} = 40 m/s

, relative retardation

a_{B A} = 4 m/s^{2}

(deceleration).

Using

v^{2} = u^{2} + 2 a s

for relative motion until relative velocity is zero:

0 = (40)^{2} - 2 (4) S ⟹ S = 200 m

This is the closing distance covered before both stop. Remaining gap:

300 - 200 = 100 m

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Single correct option

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