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Question:

A body of mass starts moving from rest along x-axis so that its velocity varies as v = a√s, where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is:

8ma4t2

18ma4t2

14ma4t2

4 ma4t2

Solution:

Velocity of body v = a√s
acceleration a' = dv/dt = a/(2√s) * ds/dt = a²/2
displacement s' = 1/2a't² = 1/2(a²/2)t²
Work done W = force × displacement
W = ma' × s' = 1/8ma⁴t²