Question

The relation between the displacement x and the time t for a body of mass 2 kg moving under the action of a force is given by x=t^(3)//3 , where x is in metre and t in second ,Calculate the work done by the body in first 2 seconds.

Answer 1

Answer:

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Explanation:

Given that,

Mass M=2kg

Displacement = x

Time t=2s

Now, the displacement is

x= t^3/3

On differentiate

dt/dx

=

3

3t

2

dt

v=t

2

dt

Again differentiate

dt

dv

=2tdt

a=2tdt

Now, the force is

F=ma

F=2×2t

F=4t

Now, the work done is

dW=F⋅dx

dW=4t×t

2

dt

dW=4t

3

dt

Work done during t = 0 to 2 sec is found by integration

∫dW=

0

∫

2

4t

3

dt

W=[(2)

4

−0]

W=16J

Hence, the work done is 16 J

Answer 2

Answer:

Explanation:

the work done will be = 4 kg /mg sq