The displacement of a body of mass 3 kg under the action of a force is S = t²/3 metre. The work done in time 2

Question 29 of 31

Q. The displacement of a body of mass 3 kg under the action of a force is S = t²/3 metre. The work done in time 2s by the same force in (J) is

(a) 2

(b) 3.8

(d) 2.66

West Bengal WbchseWest Bengal HS First Year (WBCHSE Class XI) Annual Examination 2018MCQ· 1mImportance★★★★★

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Work done equals the change in kinetic energy — find v(t) by differentiating S(t), then use W=ΔKE.

Given $S=\dfrac{t^2}{3}$ m, $m=3$ kg. The body starts from rest ( $S(0)=0,\ v(0)=0$ ).

Velocity: $v=\dfrac{dS}{dt}=\dfrac{2t}{3}$

At $t=2$ s: $v=\dfrac{2\times2}{3}=\dfrac{4}{3}$ m/s

By the work-energy theorem, the work done by the force equals the kinetic energy gained (since it started from rest): …

Q.The displacement of a body of mass 3 kg under the action of a force is S = t²/3 metre. The work done in time 2s by the same force in (J) is