A body of mass 6kg is under a force which causes displacement in it given by S=t24 metres where t is time. The work done by the force in 2 seconds is
Question
A body of mass 6kg is under a force which causes displacement in it given by S=t24 metres where t is time. The work done by the force in 2 seconds is
Solution
The work done by a force is given by the formula:
W = F * d
where W is the work done, F is the force, and d is the displacement.
Given that the displacement S = t^2/4, we can find the displacement at t = 2 seconds:
S = (2^2)/4 = 1 meter
The force F can be found using Newton's second law, F = m * a, where m is the mass and a is the acceleration.
The acceleration a is the derivative of the displacement with respect to time. So, a = dS/dt = t/2. At t = 2 seconds, a = 2/2 = 1 m/s^2.
So, F = m * a = 6 kg * 1 m/s^2 = 6 N.
Finally, we can find the work done:
W = F * d = 6 N * 1 m = 6 Joules.
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