Question

A driver applies the brakes on seeing the red traffic signal $400\text{ m}$ ahead. At the time of applying the brakes, the vehicle was moving with a speed of $54\text{ km/h}$ and retards uniformly at $0.3\text{ m/s}^2$. The distance of the vehicle from the traffic signal when it stops is

• A. $25\text{ m}$
• B. $375\text{ m}$
• C. $350\text{ m}$
• D. $50\text{ m}$

Hint:

Be sure to read the final question carefully! Calculating a stopping distance of $375\text{ m}$ might tempt you to select option (B) immediately. Always double-check whether the question is asking for the distance traveled ($375\text{ m}$) or the remaining distance from the target object ($400 - 375 = 25\text{ m}$).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A vehicle at 54 km/h brakes with deceleration 0.3 m/s² 400 m before a red light; find the remaining distance when it stops.

Step 2: Key Formula or Approach:
Convert speed to m/s (×5/18), then use v² = u² + 2aS to find stopping distance S. Remaining distance = 400 – S.

Step 3: Detailed Explanation:
u = 54 × 5/18 = 15 m/s. 0 = 225 – 0.6S → S = 225/0.6 = 375 m. Remaining = 400 – 375 = 25 m.

Step 4: Final Answer:
The vehicle stops 25 m from the signal, matching option (A).