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How to Use the Acceleration Formula

By Kathy Foust

Having some trouble understanding the acceleration formula? This study guide will walk you through all the steps.

Acceleration is known as the time rate of change in velocity as stated in the study guide on motion.

Acceleration is caused by a change in speed (which also means a change in velocity since speed is part of velocity.), a change in direction or both. Average acceleration is found using the average acceleration formula which is described below.

Acceleration Formula

To find average acceleration, you must have constant acceleration from the time that the change in velocity occurs until the change in velocity stops. For these equations we are are going to assume constant acceleration or the uniform change in velocity. This is always necessary when working with mathematical formulas--such as the formula for acceleration--and is what most textbooks use as well. Let's try the acceleration formula below.

  • To begin with, the acceleration formula is expressed as average acceleration=change in velocity/time for change to occur.

  • A car at rest accelerates uniformly on a straight track and reaches a speed of 70 km/h in 5.0 seconds. What is the acceleration?

  • To begin with we must change the km/h to m/s using the conversion formula 70 x .278= 19.46 m/s

  • We need to find the change in velocity by subtracting the end velocity from the beginning velocity.

  • We know both of the amounts because the problem states the car was "at rest" and therefore had a 0 change in velocity at that moment.

  • We also know that the car was traveling on a straight track which also tells us there was no change in direction.

  • The speed attained was 19.46 m/s, so 19.46 m/s - 0 m/s= 19.46 m/s in 5.0 seconds was the change in velocity from beginning to end.

  • Use the acceleration formula (19.46 m/s) / 5.0 s = 3.892 m/s2 where 19.46 m/s=change in velocity and 5.0 s is the time for the change to occur.

  • Following the steps for average acceleration, we find the answer to be 3.892 m/s2.

  • Round the answer down to significant numbers to get the answer of 3.9 m/s2.

The main things to remember when dealing with the acceleration formula is that the changes and movements in the formula must be constant and must be changes in velocity. Each change needs to be measured and the formula done for each one.