An object with mass 500 g moves along x-axis with speed v = 4√x m/s. The force acting on the object is :

Solution

Physics sir · 3 steps

Speed is given as a function of position, so use a = vdv/dx to get the acceleration.

1. Square the speed. From v = 4√x we get v² = 16x. Squaring first removes the square root and makes the derivative easy.

   a = vdv/dx = 1/2d(v²)/dx = 1/2 × 16 = 8 m s⁻²

2. Constant acceleration. The acceleration does not depend on x, so it is the same everywhere. This matches v² = 2ax for a body starting from rest at x = 0: here 2a = 16.
3. So. With m = 500 g = 0.5 kg, the force is F = ma = 0.5 × 8 = 4 N, option (b).

The idea to keep. When v is given in terms of x, use a = vdv/dx, or the shortcut a = 1/2d(v²)/dx. Any v² ∝ x means constant acceleration.

Answer from the NTA final answer key. Solution by PrepWiser.