acceleration

[noun]

The change in an object's velocity over time, measured in distance per unit time per unit time (for example meters per second per second or \(\frac{m}{s^2}\)). Compare to velocity. Acceleration (a) is calculated by dividing the change (symbolized by Δ, the Greek letter delta) in velocity (v) by the change in time (t):

This can also be written as:

\(a = \frac{v_2 - v_1}{ t_2 - t_1}\), where \(v_1\) and \(t_1\) denote the starting velocity and time and \(v_2\) and \(t_2\) denote the ending velocity and time.

To illustrate, imagine a car speeding up (accelerating) from a stand still (0 meters/second) to a speed of 15 meters/seconds over the course of 5 seconds. The car's total increase in velocity is 15 meters/second. During each of the 5 seconds that the car is accelerating, its velocity increases by 3 meters/second until it reaches its top speed. (After one second the car is traveling at a velocity of 3 meters/second; after 2 seconds, it's traveling at a velocity of 6 meters/second, and so on). Therefore, the car's rate of acceleration is 3 meters per second per second or 3 \(\frac{m}{s^2}\). Using the equation above: