A force `F=(2thati+3t^(2)hatj)`N acts on an object moving in XY-plane. Find the magnitude of change in momentum of the object in the time interval t=0 to t=2s.

Explanation

Given
`vecF=2t hati+3t^(2)hatj`
`rArr (d vecp)/(dt)=2t hati+3t^(2)hatj`
`rArr d vecp=2t dt hati+3t^(2)dt hatj`
`rArr int d vecp=2 int_(0)^(2) t dt hati+3int_(0)^(2) t^(2) dt hatj`
`rArr Delta vecp=[t^(2)]_(0)^(2) hati+[t^(3)]_(0)^(2) hatj`
`rArr Delta vecp=4hati+8hatj`
`rArr |Delta vecp|=sqrt(16+84)`
`=sqrt(80)`
`=9 "kg m"//s`