Problem 68.

The acceleration of an object as a function of time is . Determine the

(a) velocity and

(b) the position of the object as a function of time

if it is located at x = 2 m and has a velocity of 3 m/s at time t = 0 s.

Solution:

(a) By definition the velocity of the object is the integral of acceleration with respect to time:

where is the initial velocity (at t=0).

(b) The position can found as an integral of velocity with respect to time:

where is the initial position (at t=0) of the object.