If a ball is given a push so that it has an initial velocity of 5 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s (t) = 5t + 2t2 (a) Find the velocity after 2 seconds.

v = 13 m/s

Explanation:

Velocity is defined as the derivative of displacement with respect to time

v = ds/dt

Known data

s (t) = 5t + 2t² : distance that the ball has rolled after t seconds

vi = 5 m/s : initial velocity

t = 2 s

Problem develoment

s (t) = 5t + 2t²

v = ds/dt = 5 + 4t : velocity of the ball in function of the time

We replace t = 2 s in the equation of velocity

v = 5 + 4 (2)

v = 13 m/s : velocity after 2 seconds