For a particle, the momentum p varies with time t such that dp dt = (10 N ) + (2 N/s )t . Assuming the momentum is zero at t = 0 , determine the momentum at t = 10 s .

Step-by-step solution

Given dp dt = 10 + 2t dp = (10 + 2t) dt Integrating both sides from t = 0 to t = 10 s : ₀^ p dp = ₀¹⁰ (10 + 2t) dt p = [ 10t + t^2 ]₀¹⁰ p = 10(10) + (10)^2 p = 100 + 100 = 200 kg m/s