Question

A body of mass `1kg ` begins to move under the actio of a time dependent force `vec(F)=(2t hat(i)+3t^(2) hat(j))N`, where `hat (i) ` and `hat(j)` are unit vectors along `X` and `Y` axis. What does will be developed by the source at time `t` ?
A. `(2t^(2)+4r^(4))W`
B. `(2t^(2)+3r^(4))W`
C. `(2t^(3)+3r^(5))W`
D. `(2t+3r^(3))W`

Answer 1

Correct Answer - C
Here, `m=1kg`
`vec(F)=(2t hat(i)+3t^(2)hat(j))N,P=?`
From `F=ma=m(dupsilon)/(dt)`
`(dupsilon)/(dt)=(F)/(m)=(2that(i) +3t^(2)hat(j))/(1)`
`=(2t hat(i)+3t^(2)hat(j))m//s^(2)`
`dupsilon=(2that(i)+3t^(2)hat(j))dt`
`upsilon=int (2that(i)+3t^(2)hat(j))dt`
`=(2t^(2))/(2)hat(i)+(3t^(3))/(3)hat(j)=(t^(2)hat(i)+t^(3)hat(j))`
Now, `P=vec(F). vec(upsilon)=(2that(i)+3t^(2)hat(j)).(t^(2)hat(i)+t^(3)hat(j))`
`P=(2t^(3)+3t^(5))"watt"`