Question

A body of mass 3 kg is under a constant force which causes a displacement s in m in it, given by the relation s= t, where t is in seconds. Work done by the force in 2 seconds is: [aipmt, 2006)

Answer 1

Answer:

To find the work done we have to find:

1) Force

2) Displacement

Then after using ;

Work done = Force × displacement .

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# Finding FORCE :

We are given displacement-time relation :

s = (1/3) × t²

Differentiating it wrt time t ; we get velocity - time relation :-

v = (2/3)×t

again differentiating above wrt time t ; we get acceleration of body :-

a = 2/3 m/s²

Now ;

Force = mass × acceleration

= 3× (2/3) = 2 N

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#Finding Displacement

using displacement-time relation and putting the t = 2 ; we get the displacement the body covers in 2 seconds .

s = (1/3) (2)²

s = 4/3 m

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Now work done = 2 × 4/3

= 8/3 J