Question

A body of mass 9 kg is under a force that causes displacement in it given by s = `5t^2"/"6` metre where t is time. The work done by the force in 2 seconds is ______

Options

• 10 J

• 20 J

• 25 J

• 50 J

Answer 1

A body of mass 9 kg is under a force that causes displacement in it given by s = `5t^2"/"6` metre where t is time. The work done by the force in 2 seconds is 50 J.

Explanation:

s = `(5t^2)/6`

∴ ds = `(5t)/3`dt

a = `(d^2s)/(dt^2) = d/dt[(ds)/(dt)] = d/dt[(5t)/3] = 5/3`

∴ F = ma = `9 xx 5/3 = 15` N

Now, W = `int_0^1F ds = int_0^2 15((5t)/3)dt`

= `25[t^2/2]_0^2 = 25/2[(2)^2 - (0)^2]` = 50 J