Speed, velocity and acceleration proof

Question

Show that, if an object is moving on a straight line, then its speed is increasing when its velocity v and its
acceleration a have the same sign, and its speed is decreasing when v and a have opposite sign.

Answer 1

Acceleration = Velocity/time

 

Keep in mind that acceleration and velocity are directly proportional related to each other.

 

When an object's velocity increases in one direction, it accelerates in the same direction the object moves because a force pushes it in that direction.  Suppose that same object is moving at a constant speed in one direction, but a force pushes the object in the opposite direction.  It decelerates slowing the object down, so the velocity is decreasing.