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The velocity of a body of mass 2 kg as...

The velocity of a body of mass ` 2 kg ` as a function of t is given by ` upsilon(t) = 2t hati + t^(2) hatj ` Find the momentum and force acting on it at time `t = 2 s`.

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Given , mass of the body m = 2kg
Velocity of the body v(t) = `2 t hati + t^(2) hatj`
`therefore` Velocity of the body at t = 2s
`v = 2 xx 2 hati + (2)^(2)hatj = (4hati + 4 hatj)`
Momentum of the body (p) = mv = `2(4hati + 4hatj) = (8hati + 8hatj)` kg-m/s
Acceleration of the body (a) = `(dv)/(dt)`
= `(d)/(dt) (2t hati + t^(2) hatj)`
= `2 (hati + 2t hatj)`
At t = 2 s
a = `(2hati + 2 xx 2hatj)`
= `(2hati + 4 hatj)`
Force acting on the body (F) = ma
= `2 (2hati + 4 hatj)`
= `(4hati + 8 hatj )N`
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