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Question
The velocity of a body of mass 2 kg as a function of t is given by `v(t) = 2t hati + t^2hatj`. Find the momentum and the force acting on it, at time t = 2s.
Solution
Given, the mass of the body m = 2 kg.
Velocity of the body `v(t) = 2t hati + t^2hatj`
∴ The velocity of the body at t = 2s
v = `2 xx 2hati + (2)^2 hatj`
= `(4hati + 4hatj)`
The 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^2hatj)`
= `(2hati + 2t hatj)`
At t = 2s
a = `(2hati + 2 xx 2hatj)`
= `(2hati + 4hatj)`
Force acting on the body (F) = ma
= `2(2hati + 4hatj)`
= `(4hati + 8hatj) N`
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