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A body of mass 4 kg is acted upon by a f...

A body of mass 4 kg is acted upon by a force. The position of body with respect to time is denoted by `x = (t^4)/4`. The work done by the force in first three seconds can be expressed in SI system as

A

1458 J

B

729 J

C

54 J

D

27 J

Text Solution

Verified by Experts

The correct Answer is:
A
Force produces change in kinetic energy. Initially, KE=0 because body is at rest. Velocity is gained due to application of force.
Given, `x = (t^4)/4 therefore (dx)/(dt) = (4t^3)/(4) = t^3`
`therefore` Velocity gained `v = t^3`
`t = 3s`
Velocity = `27 m//s`
`KE = 1/2 mv^2 = 1/2 xx 4 xx (27)^2`
`= 2 xx 27 xx 27 = 1458 J `
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