Question

A driver applies the brakes on seeing the traffic signal 400 m ahead. At the time of applying brakes, the vehicle was moving with 15 m/s and retarding at 0.3 m/s². The distance covered by the vehicle from the traffic light one minute after application of brakes is

• A. 375 m
• B. 360 m
• C. 40 m
• D. 25 m

Answer 1

Answer: (D)

25 m

Answer 2

Here's the breakdown of the solution:

1. Calculate the stopping time:

   The vehicle decelerates at 0.3 m/s² from an initial speed of 15 m/s. The stopping time $t_{\text{stop}}$ is given by:

   $$t_{\text{stop}} = \frac{15}{0.3} = 50\,\text{s}$$

   Since 1 minute = 60 s, the vehicle stops at 50 s and remains stationary for the remaining 10 s.

2. Calculate the stopping distance:

   Distance covered until the vehicle stops is obtained from:

   $$v^2 = u^2 + 2aS \implies 0 = 15^2 - 2(0.3)S$$

   which gives

   $$S = \frac{15^2}{2 \times 0.3} = \frac{225}{0.6} = 375\,\text{m}$$

3. Calculate the final distance from the traffic signal:

   The distance from the traffic signal 1 minute after applying brakes is:

   $$\text{Distance from signal} = 400\,\text{m} - 375\,\text{m} = 25\,\text{m}$$