An object that moves at a constant speed ( or velocity ) will continue doing so until it is acted upon by a force. Whether such an object speeds up or slows down after being impacted by a force, the change in motion is called an acceleration. Typically, a decrease in motion is referred to as a “ deceleration “.
Q: A batter hits a 0.15 kg baseball traveling 45 meters per second westward. The after-impact velocity of the ball is 35 meters per second to the east. The ball-to-bat collision lasts 1.0 x 10-2 seconds. What is the magnitude and direction of the baseball’s average acceleration while it is in contact with the bat?
A: Notice that the baseball begins traveling westward and ends up traveling eastward. For this reason, the respective motions represent velocities that possess both magnitude and direction. We are at liberty to choose either east or west as the negative or positive direction; however, once we’ve done so, we must be sure to abide by these attributions throughout the problem-solving process. We are given two velocities and a time interval that the ball and bat are in contact with one another. For this reason, we use an equation that relates what is given to a value that must be determined:
vf = vo + at
Let’s assign a negative sign to the westward velocity and a positive sign to the eastward velocity that is provided:
35 m/s = – 45 m/s + ( a )( 1.0 x 10-2 s )
80 m/s = ( a )( 1.0 x 10-2 s )
a = ( 80 m/s / 1.0 x 10-2 s )
a = 8,000 m/s2
The acceleration value is positive, and this is indicative of the ball moving eastward after the collision occurs. Notice how the mass of the ball was not included in our final calculations. In kinematics, we are primarily concerned with observations of what happens to the motion of an object ( or objects ) without regard to the magnitude of the forces that give rise to our observations. A larger baseball would have to be impacted with a proportionally larger bat for the same duration of time to get the same results, but these worries are of no concern to us…yet.
RENAISSANCE PHYSICS 