Multiple choice

A body is moving with a speed of $1$ m/s and a constant force $F$ is needed to stop it in a distance $x$. If the speed of the body is $3$ m/s the force needed to stop it in the same distance $x$ will be :

  1. $1.5\  F$
  2. $3\  F$
  3. $6\  F$
  4. $9\  F$
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D Correct answer
Explanation

Work done to stop the body equals its kinetic energy: F * x = (1/2) * m * v^2. Since F * x is constant, F is proportional to v^2. If speed increases from 1 to 3 (a factor of 3), the force must increase by a factor of 3^2 = 9.

AI explanation

The equation of motion relating force to stopping distance is v^2 = 2as, where acceleration a equals force F divided by mass m. For the first case, 1^2 = 2(F/m)x, and for the second case with a higher initial speed, 3^2 = 2(F'/m)x. Dividing the second equation by the first gives F'/F = 9 / 1. The required force is 9 F.

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