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

To determine the distance between two cars upon braking to a stop, we follow these steps:

1. Both vehicles are initially approaching each other at a velocity of \(20 \, \text{m/s}\).
2. The initial separation between the cars is \(300 \, \text{m}\).
3. Both cars initiate braking, experiencing a deceleration (negative acceleration) of \(2 \, \text{m/s}^2\).

We utilize the kinematic equation for constant acceleration:

\(v^2 = u^2 + 2as\)

• Where:
• \(v\) represents the final velocity, which is 0 m/s as the cars halt.
• \(u\) denotes the initial velocity, given as \(20 \, \text{m/s}\).
• \(a\) is the acceleration, specifically \(-2 \, \text{m/s}^2\).
• \(s\) signifies the distance covered by each car from the point of braking until it stops.

The equation is applied independently to each car:

1. For a single car:
   • \(0 = (20)^2 + 2(-2) \times s_1\)
   • \(0 = 400 - 4s_1\)
   • Solving for \(s_1\) yields: \(s_1 = \frac{400}{4} = 100 \, \text{m}\)
2. Each car travels a distance of \(100 \, \text{m}\) before coming to a complete stop.

The cumulative distance covered by both cars totals \(100 \, \text{m} + 100 \, \text{m} = 200 \, \text{m}\). Given the initial separation of \(300 \, \text{m}\), the remaining distance between the cars when they stop is calculated as:

\(300 \, \text{m} - 200 \, \text{m} = 100 \, \text{m}\)

Consequently, the distance separating the cars when they achieve a standstill is 100 m.