The relation between the displacement x and the time t for a body of mass 2kg moving under the action - Physics - Work Energy And Power

Question

The relation between the displacement x and the time t for a
body of mass 2kg moving under the action of force is given by
x=t3/3 , where x is in metre and t in second , calculate
the work done by body in first 2 seconds

Somnath physics · Accepted Answer

Here,

Mass, m = 2 kg

Displacement is given as, x = t3/3

So, d(x)/dt = (3)(t2)/3 = t2

=> d2(x)/dt2 = 2t

=> a = 2t

This is the acceleration of the body

Now,

For a small displacement â€˜dxâ€™
the work done is,

dW = F dx

=> dW = (ma) d(t3/3)

=> dW = 2(2t)(3t2/3)

=> dW = 4t3

The relation between the displacement x and the time t for a body of mass 2kg moving under the action of force is given by x=t3/3 , where x is in metre and t in second , calculate the work done by body in first 2 seconds.

The relation between the displacement x and the time t for a body of mass 2kg moving under the action of force is given by x=t³/3 , where x is in metre and t in second , calculate the work done by body in first 2 seconds.