In physics, velocity is defined as the change in distance traveled by an object with respect to time whereas acceleration is defined as the rate of change in velocity of this object with respect to time.

Average acceleration just like average velocity is defined over some specified period of time with a beginning and ending time period. When acceleration increases, a positive algebraic sign will be associated, whereas an acceleration decrease (deceleration) will be accompanied by a negative algebraic sign. In other words, when you are driving a car and are pressing your foot harder on to the gas pedal you will be traveling at a quicker rate than you were before or accelerating. If you are in this same car and are pressing the brake pedal to come to a stoplight you are decelerating or experiencing negative acceleration.

The formula for acceleration can be computed as follows using the initial and final velocities (V_{i} and V_{f }) of the time period and the initial and final times (T_{i} and T_{f }).

A = (V_{f }– V_{i})/(T_{f }– T_{i}).

Let’s consider an example. You are driving on a straight stretch of highway down an interstate road traveling at 85 mph at 4:00 PM, you then see a police car sitting by the side of the road and so you apply your foot to the brake to decrease your velocity to 65 mph by 4:06 PM. From 4:00 to 4:06 PM what was your average acceleration?

Your acceleration, A = (V_{f }– V_{i})/(T_{f }– T_{i}) = [(65 mi/hr – 85 mi/hr)/(6 min.)](60 min. / 1hr)

A = (-3.33 mi/hr-min.)/(60 min. / 1 hr) = -200 miles/hour^{2}

So your acceleration is -200 miles/hour^{2}. This negative value indicates that you were reducing your velocity and therefore decelerating. Had you speed up to try to out run the police officer, which you should never do, you would have been accelerating.

Let’s see another situation. You are driving along the same straight stretch of highway, there is road construction and you are traveling at the posted speed of 55 mph at 5:30 PM, then you transition out of the construction zone and reach the posted speed of 70 mph at 5:34 PM. During this time period, what is your average acceleration? In this case, you are increasing in your speed and are therefore accelerating, so the value of acceleration will be positive.

Your acceleration, A = (V_{f }– V_{i})/(T_{f }– T_{i}) = [(70 mi/hr – 55 mi/hr)/(4 min.)](60 min. / 1hr)

A = (3.75 mi/hr-min.)/(60 min. / 1 hr) = 225 miles/hour^{2}

This quite simply is what acceleration is.

Source:

Serway, R. A., Beichner, R. J., & Jewett, J. W. (2000). Physics For Scientists and Engineers, Volume 1 (5^{th} Ed.). Orlando, FL: Saunders College Publishing.