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Figure shows (vx,t) and (vy,t) diagram f...



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

Text Solution

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Consider figure(a) `" " v_(x) = 2t` for `0 lt t lt 1s`
= `2(2-t)` for `1 lt t lt 1s`
= 0 for t `gt` 2s.
From figure (b) `" " v_(y) = t ` for `0 lt t lt 1s`
= 1 for t `gt` 1s
`F_(x) = ma_(x) = m (dv_(x))/(dt)`
`= 1 xx 2 " for" 0 lt t lt 1s`
`= 1(-2) " for" 1 lt t lt 2s`
`" for" 2 lt t`

`F_(y)=ma_(y)=m(dv_(y))/(dt)`
`=1xx1 " for " 0 lt t lt 1s = 0 " for " 1 lt t`
Hence, `F= F_(x) hati+F_(y) hatj`
`=2 hati + hatj " for" 0 lt t lt 1s `
`= -2 hati " for " 1 lt t lt 2s`
`=0 " for " t gt 2s `
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