Calculus Question

Question

A particle is moving with acceleration a(t)=24t+14. its position at time t=0 is s(0)=13 and its velocity at time t=0 is v(0)=17. What is its position at time t=5? 

Answer 1

That means that its velocity at any time t >= 0 is v(t) = integral of a(t) = 24t²/2 + 14t + v(0) = 12t² + 14t + 17, and its position at any time t >= 0 is s(t) = integral of v(t) = 12t³/3 + 14t²/2 + 17t + s(0) = 4t³ + 7t² + 17t + 13, so the position of the particle at time t = 5 is the following:

s(5) = 4*5³ + 7*5² + 17*5 + 13 = 4*125 + 7*25 + 85 + 13 = 500 + 175 + 98 = 773.