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

Answer: (C)

100 m

Answer 2

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.