Question

Under the action of force, a 2 kg body moves such that x is a function of time given by x=t³/3, x in metre, t in seconds, find the work done in first two seconds.____

Answer 1

The work done in the first two seconds is 48 Joules.

Step-by-step explanation:

In order to find the work done by the force, we need to integrate the force with respect to distance. The formula for work is given by:

W = ∫F dx

In this case, the force acting on the body is given by F = ma, where m = 2 kg and a = d²x/dt². Integrating this force over the given distance x = t³/3, we can find the work done. Let's calculate:

W = ∫(2)(d²x/dt²) dx

W = ∫(2)(2t) (3t²/3) dt = 2∫6t³ dt

W = 12(t⁴/4) = 3t⁴

Now we need to find the work done in the first two seconds, so we substitute t = 2 into our equation:

W = 3(2)⁴ = 3(16) = 48 J

Therefore, the work done in the first two seconds is 48 Joules.