Question

A force F is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of the cart at t = 5 sec is ______.

 

Options

• 10 m/s

• 8.33 m/s

• 2 m/s

• Zero

Answer 1

A force F is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of the cart at t = 5 sec is 8.33 m/s.

Explanation:

∴ Parabola has equation,

.............(1)

⇒ 50 = k(5)²

⇒ k = 2

∴ F = 2t² .................(2)

⇒ `m(dv)/(dt) = 2t^2`

⇒ `10int_0^v dv = 2int_0^5 t^2 dt`

⇒ `10 v = 2(t^3/3)_0^5`

⇒ v = 8.33 m/s