Question

The momentum ρ of a paricle changes with time t according to the relation dp/dt = (10 N) + (2 N/s)t . If the momentum is zero at t = 0 , what will be the momentum at t = 10 s ?

Answer 1

Thanks for asking the question!

ANSWER::

dp/dt = (10 N) + (2 N/S)t

At t = 0 , momentum is zero.
At t = 10 seconds , momentum will be

dp/dt = [(10 N) + 2Ns t]dt

ₐ∫ᵇ dp = ₀∫¹⁰ 10 dt + ₀∫¹⁰ (2t dt) 
         = ₀[10t]¹⁰ + ₀[2t²/2]¹⁰ = 200 kg m/s

Hope it helps!