An object of mass 3 kg starts from rest under a time-dependent force F = 6t² $\hat{i}$ + 4t $\hat{j}$ N. Its velocity at t = 3 s is:
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An object of mass 3 kg starts from rest under a time-dependent force F = 6t² i ^ \hat{i} i ^ + 4t j ^ \hat{j} j ^ ​ N. Its velocity at t = 3 s is:

G1 Physics · Accepted Answer

Acceleration a=F/m=2t² i +(4t/3)j. Integrating from t=0 to 3 s: vₓ=∫2t²dt=2(3³)/3=18; vᵧ=∫(4t/3)dt=(2/3)(3²)=6. Thus v=18i+6j m s⁻¹. Answer: B.

An object of mass 3 kg starts from rest under a time-dependent force F = 6t² i ^ \hat{i} i ^ + 4t j ^ \hat{j} j ^ ​ N. Its velocity at t = 3 s is: