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, `F=(2thati+3t^(2)hatj)N" " implies(dp)/(dt)=2thati+3t^(2)hatj`
`implies dp=2tdthati+3t^(2)dthatj`
`implies intdp=2int_(0)^(2)tdthati+3int_(2)^(0)t^(2)dthatj`
`implies Delta p=[t^(2)]_(0)^(2)hati+[t^(3)]_(0)^(2)hatj implies Delta p=4hati+8hatj`
`implies abs(Deltap)= sqrt(16+64)=sqrt(80)~~9kg ms^(-1)`