Question

Two cars are travelling towards each other at a speed of \( 20 \, \text{m/s} \) each. When the cars are \( 300 \, \text{m} \) apart, both the drivers apply brakes and the cars retard at the rate of \( 2 \, \text{m/s}^2 \). The distance between them when they come to rest is:

• A. 200 m
• B. 50 m
• C. 100 m
• D. 25 m

Answer 1

The Correct Option is C

Let the distance between the cars when they come to rest be \( d \). Each car has an initial speed of 20 m/s. The deceleration \( a \) is \(-2 \, \text{m/s}^2\).

Using the equation of motion:

\( v^2 = u^2 + 2ad, \)

where \( v = 0 \) (final speed), \( u = 20 \, \text{m/s} \) (initial speed), and \( a = -2 \, \text{m/s}^2 \), we get:

\( 0 = 20^2 + 2(-2)d \quad \Rightarrow \quad 0 = 400 - 4d \quad \Rightarrow \quad d = 100 \, \text{m}. \)

Since the two cars are moving towards each other, the total distance covered by both cars is \( 100 + 100 = 200 \, \text{m} \), so the distance between them when they come to rest is 100 m.