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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 = 2 kg.
Velocity of the body `v(t) = 2t hat(i) + t^(2) hat(j)` `:.` Velocity of the body at t = 2s
`v = 2 xx 2 hat(i) + (2)^(2) hat(j) = (4 hat(i) + t^(2) hat(j))`
Momentum of the body (p) = mv `= 2 (4 hat(i) + 4 hat(j)) = (8 hat(i) + 8 hat(j)) kg - m//s`
Acceleration of the body `(a) = (dv)/(dt)` `= (d)/(dt) (2 t hat(i) + t^(2) hat(j))` `=(2 hat(i) + 2t hat(j))`
At t = 2s `2 = (2 hat(i) + 2 xx 2 hat(j))`
Force acting on the body (F) = ma `= 2(2hat(i) + 4 hat(j)) = (4 hat(i) + 8 hat(j)) N`
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