Calculating Acceleration

Acceleration is the rate at which velocity changes. You calculate acceleration for straight-line motion by dividing the change in velocity by the total time. If a is the acceleration, vⁱ is the initial velocity, v^f is the final velocity, and t is total time, then this equation can be written as follows.

Notice in this formula that velocity is in the numerator and time is in the denominator. If the velocity increases, the numerator is positive and thus the acceleration is also positive. For example, if you are coasting downhill on a bicycle, your velocity increases and your acceleration is positive. If the velocity decreases, then the numerator is negative and the acceleration is also negative. For example, if you continue coasting after you reach the bottom of the hill, your velocity decreases and your acceleration is negative.

Remember that acceleration and velocity are both vector quantities. Thus, if an object moving at constant speed changes its direction of travel, there is still acceleration. In other words, the acceleration can occur even if the speed is constant. Think about a car moving at a constant speed as it rounds a curve. Because its direction is changing, the car is accelerating.

To determine a change in velocity, subtract one velocity vector from another. If the motion is in a straight line, however, the velocity can be treated as speed. You can then find acceleration from the change in speed divided by the time.