3.5:
Average Acceleration
Acceleration is defined as the change in velocity with time. It is a vector quantity and involves a change in magnitude or direction or both.
For example, a woman is walking at 5 km/h towards the east. She stops and returns, walking at 5 km/h towards the west. Here, the woman's velocity changed due to a change in direction, though its magnitude is the same in both directions, which resulted in acceleration.
Acceleration is expressed in meters per second squared and can be interpreted from the velocity versus time graph where velocity is on the y-axis and time is on the x-axis.
For instance, a woman is walking on a road. At point P1, she has a velocity of v1x at time t1. And after some time at t2, her velocity is v2x at point P2. The change in her velocity is given by Δv in a time interval of Δt.
Thus, the average acceleration of the woman moving from point P1 to P2 is the change in the x-component of velocity, divided by the time interval. It is also given by the slope of the line P1P2.
3.5:
Average Acceleration
The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic physics. In everyday conversation, to accelerate means to speed up. For instance, we are familiar with the acceleration of our car; the harder we apply our foot to the gas pedal, the faster we accelerate. The greater the acceleration, the greater the change in velocity over a given time. Acceleration is widely seen in experimental physics. In linear particle accelerator experiments, for example, subatomic particles are accelerated to very high velocities in collision experiments, which tell us information about the structure of the subatomic world as well as the origin of the universe. In space, cosmic rays are subatomic particles that have been accelerated to very high energies in supernovas (exploding massive stars) and active galactic nuclei. It is important to understand the processes that accelerate cosmic rays, because these rays contain highly penetrating radiation that can damage electronics on spacecraft, for example.
Average acceleration is the rate at which velocity changes. Recall that velocity is a vector—it has both magnitude and direction—which means that a change in velocity can be a change in magnitude (speed), or a change in direction. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h due west, their velocity has changed as a result of the change in direction, even though the magnitude of the velocity is the same in both directions. Thus, acceleration occurs when velocity changes in magnitude (an increase or decrease in speed) or in direction, or both.
This text is adapted from Openstax, University Physics Volume 1, Section 3.3: Average and Instantaneous Acceleration.