The velocity of a body of mass 2 kg as a function of t is given by `v(t) = 2t hati + t^(2)hatj` . Find the momentum and the force acting on it, at time t = 2s.

Explanation

Mass of the body m=2 kg
velocity of the body v (t ) = (2t ) `hat(j) + (t^(2) hat(j))`
Velocity of the body at t= 2 s
`=4hat(j ) + 4hat(j )`
Momentum of body `vec( p ) =mv = 2 (4hat(j ) + 4hat(j ))`
Acceleration of body
`a= (d v)/( dt )`
`=(d )/(dt ) (2t hat(j ) + t^(2) hat(j ))`
At t =2s
`(2hat(i ) + 4hat(j ) )`
Force acting on the body ( F ) =ma
`=(4hat(i ) + 8hat(j ))N`