The acceleration of a moving body at any ‘t’ is given by $\vec{a}$ = (4t)î + (3t²)ĵ m/sec². If $\vec{u}$ = 0 then find the velocity (in m/s) of the particle at 4 sec.
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Question

The acceleration of a moving body at any ‘t’ is given by a ⃗ \vec{a} a = (4t)î + (3t²)ĵ m/sec². If u ⃗ \vec{u} u = 0 then find the velocity (in m/s) of the particle at 4 sec.

G1 Physics · Accepted Answer

Integrate the acceleration components from t = 0 with initial velocity zero: vₓ = ∫4t dt = 2t² and vᵧ = ∫3t² dt = t³. At t = 4 s, v⃗ = 32î + 64ĵ m/s. Hence option B.