Multiple choice

A car which is at rest starts accelerating at the rate of 2 m/s2 when a motorcycle travelling with a constant speed of 54 kmph crosses it. The time at which the car will catch the motor cycle is

  1. 27 seconds

  2. 15 seconds

  3. 54 seconds

  4. 15 minutes

  5. 54 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Motorcycle speed = 54 kmph = 15 m/s. Let t be the time. Distance covered by car = 0.5 * 2 * t^2 = t^2. Distance covered by motorcycle = 15 * t. Equating distances: t^2 = 15t, so t = 15 seconds.

AI explanation

First convert the motorcycle's constant speed of 54 kmph to meters per second by multiplying by 5/18, giving 15 m/s. To catch the motorcycle, the car's displacement must equal the motorcycle's displacement, so (1/2)(2)t^2 = 15t. Solving the equation t^2 = 15t yields a time of 15 seconds.

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