1.

The mass of a body is 2.5 Kg. it is in motion and its velocity `upsilon`after time t is ` upsilon = (t^3)/(3) +(t^2)/(2) +1` Calculate the force acting on the body at the time t =3 s.

Answer» Acceleration, `a = (dupsilon)/(dt) = (d)/(dt)((t^3)/(3) +(t^2)/(2) +1) = (d)/(dt)((t^3)/(3)) +(d)/(dt) ((t^2)/(2)) +(d)/(dt) (1)`
`=(1)/(3)xx3t^(3-1) +(1)/(2)2t^(2-1) +0 =t^2 +t`
When t =3 s, `a = 3^2 +3 = 12 m//s^2`
As, force = mass xx acceleration = `2.5xx12 = 30N`


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