If the velocity at t = 0 is 4 meters per second, find the velocity 2 seconds later.

Question

The acceleration of an object moving along a coordinate line is given by a(t) = (5t + 3)^-5 in meters per second per second. If the velocity at t = 0 is 4 meters per second, find the velocity 2 seconds later.

v =_____ meters per second

Answer 1

Velocity, v(t) = ∫a(t)dt

v(t)= ∫(5t+3)^-5dt = -(5t+3)^-4/20 + C

v(0) = -3^-4/20+C=4 --> C= 4+3^-4/20

v(2) = -(13)^-4/20 + C