A bus is travelling at 54 km/h. suddenly, the driver sees a stop sign 190 m in…

2023

A bus is travelling at 54 km/h. suddenly, the driver sees a stop sign 190 m in front and instantly applies the brakes. The bus retards uniformly and stops 10 m before the sign board. How much did the bus take to stop after the brakes were applied?

  1. A.

    10 seconds

  2. B.

    24 seconds

  3. C.

    15 seconds

  4. D.

    18 seconds

Attempted by 2 students.

Show answer & explanation

Correct answer: B

Step-by-Step Solution

To calculate the time the bus took to stop, we can use the equations of motion for uniform retardation.

  1. Convert speed to standard units (meters per second):

    • Initial velocity (u) = 54 km/h

    • To convert to m/s, multiply by (5 / 18):

    • u = 54 * (5 / 18) = 15 m/s.

  2. Determine the distance (s):

    • The bus stops 10 m before the sign, which is 190 m away.

    • Stopping distance (s) = 190 m - 10 m = 180 m.

  3. Find the time taken (t):

    • We know the final velocity (v) is 0 m/s (since it stops).

    • We use the kinematic relation: s = ((u + v) / 2) * t

    • 180 = ((15 + 0) / 2) * t

    • 180 = 7.5 * t

    • t = 180 / 7.5

    • t = 24 seconds.

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