Figure shows `(v_x`,t) and `(v_y`,t) diagram for a body of unit mass. Find the force as a function of time.

Explanation

Cosider figure (a)
`v_x=2t` for `0lttlt1s`
`=2(2-t)` for `1lttlt2s`
`=0` for `tlt2s`
From figure (b)`v_y=t` for `0lttlt1s`
`=1` for `tgt1s`
`F_x=ma_x=m(dv_x)/(dt)`
`=1xx2=2N` for `0lttlt1s`
`=1(-2)=-2N` for `1slttlt2s`
`=0` for `tgt2s`
`F_y=ma_y=m(dv_y)/(dt)`
`=1xx1=1N` for `0lttlt1s`
`=0` for `tgt1s`
Hence, `F=F_(x)hatii+F_(y)hatj`
`=(2hati+hatj)N` for `0lttlt1s`
`=-2hatiN` for `1slttlt2s`
`=0` for `tgt2s`