A force `2bar(i)+bar(j)-bar(k)` Newton acts on a body which is initially at rest . At the end of 20 seconds the velocity of the body is `4bar(i)+2bar(j)-2bar(k)` m/s . What is the mass of the body ?

Explanation

Force F = `2bar(i)+bar(j)-bar(k)` , time t = 20 sec .
Initial velocity `mu_(0)=0`
Final velocity `U=4bar(i)+2bar(j)-2bar(k)`
Mass of the body `m=(F)/(a)`
But acceleration a `(U-U_(0))/(t)`
`thereforem=(F.t)/(U-U_(0))=(20.|F|)/(|U-U_(0)|)`
`=(20sqrt(2^(2)+1+1))/(sqrt(4^(2)+2^(2)+2^(2))-0)=(20sqrt(6))/(sqrt(24))`
`thereforem=(20sqrt(6))/(sqrt(4xx6))=(20sqrt(6))/(2sqrt(6))=10kg. `