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Question

A ball of mass 100 g is under a force which causes a displacement S in metres, given by the relation S=t3+t2 where t is in seconds. Work done by the force in 3 seconds

A
72.45 J
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B
36.55 J
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C
20 J
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D
54.45 J
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Solution

The correct option is D 54.45 J
Given displacement of the ball, S=(t3+t2) m........(1)
dS=(3t2+2t)dt
Acceleration a=d2Sdt2=6t+2
Force acting on ball at time t, F(t)=ma=0.1(6t+2)

Work done by force at time t is given by
dW=F(t)dS=0.1(6t+2)(3t2+2t)dt
=0.1(18t3+18t2+4t)dt

Therefore, total work done by force in 3 seconds
W=dW=300.1(18t3+18t2+4t)dt
=0.1[92t4+6t3+2t2]30
=0.1[7292+162+18]
=0.1×10892=54.45 J

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