Multiple choice

A car travelling at a speed of $30\ km/h$ is brought to rest in a distance of $8\ m$ by applying brakes. If the same car is moving at a speed of $60\ km/h$ then it can be brought to rest with same brakes in

  1. $64\ m$
  2. $32\ m$
  3. $16\ m$
  4. $4\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done by brakes equals change in kinetic energy. (1/2)mv^2 = F*d. Since F is constant, d is proportional to v^2. If speed doubles (30 to 60), distance increases by 2^2 = 4 times. 8 m * 4 = 32 m.

AI explanation

Using the equation of motion v^2 = u^2 - 2as, the stopping distance is proportional to the square of the initial velocity when the deceleration is constant. The initial speed increases from 30 km/h to 60 km/h, which is a factor of two. Since the distance depends on the square of the speed, the new stopping distance is 2^2, or 4, times the original 8 m, resulting in 32 m.

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