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Question: A particle of mass 6 kg moves according to the law x = 0.2 t<sup>2</sup> + 0.02 t<sup>3</sup>. Find ...

A particle of mass 6 kg moves according to the law x = 0.2 t2 + 0.02 t3. Find the work done by the force in first 4s.

A

1.1231 J

B

2.6428 J

C

2.1324 J

D

1.6428 J

Answer

1.6428 J

Explanation

Solution

W = 12\frac { 1 } { 2 } m(vf2 – vi2)

v = dxdt=0.4t−.06t2\frac { \mathrm { dx } } { \mathrm { dt } } = 0.4 \mathrm { t } - .06 \mathrm { t } ^ { 2 }

= 12×6[(.74)2−0]=1.6428 J\frac { 1 } { 2 } \times 6 \left[ ( .74 ) ^ { 2 } - 0 \right] = 1.6428 \mathrm {~J}