Скачать или смотреть Kinematics with two different accelerations: find the total displacement.

Our given graph of acceleration vs. time shows two different values of acceleration acting for different amounts of time: 5m/s^2 for 5s followed by -3m/s^2 for 4s. We are told the object starts at the origin from rest, and we want to find the final speed and total displacement of the object.

To find the final speed, we can just find the total signed area bounded by the acceleration-time graph to get the change in velocity. Since the initial velocity was zero, the final velocity is simply equal to this delta-v. We were asked for final speed instead of velocity, but our answer is positive anyway, so we're done.

The harder part of the problem is finding the total displacement for an object with two different values of acceleration. We have to break the motion into two different parts and use the equations of kinematics to solve for the displacement and velocity at the end of the first part, then substitute those values in to the second part as initial position and velocity.