Definition of acceleration

The definition of acceleration is a little more complex than that of the speed or the velocity. May be if you clearly see the difference between the two, it will help you to avoid common pitfalls. So what is the difference between speed and acceleration?

The speed is how fast you can get somewhere.

The word somewhere tells you that some distance is involved.

The word fast tells you that time is involved.

For example, let's say that a store is 8 miles away and your Toyota camry can make it to the store in 10 minutes.

Below are different ways to express the rate or the speed at which the car can cover this distance:

  • 8 mile per 10 minutes
  • 16 miles per 20 minutes
  • 24 miles per 30 minutes
  • 48 miles per hour  
You can also write  
48 / 1

And this is where the definition of speed came from.

Speed =
d / t

Now, if you want to know how fast the speed can change to take you to the store, you are talking about acceleration.

Here is a situation where you will care about the acceleration of your car.


Suppose on your way to the store, there is one last traffic light. You stop at that traffic light and a ford mustang Shelby stops next to you and wants to race you.

You are no match if you are driving a pickup truck that can do 0 to 60 miles per hour in 12 second because the mustang can do the same in 4 second. 

See below a description of the acceleration or how fast the speed of the mustang is changing.

15 miles per hour           1 second

30  miles per hour          2 seconds 

45 miles per hour           3 seconds

60 miles per hour           4 seconds

Every second, the speed of the mustang increases or changes by 15 miles per hour.

See below a description of the acceleration or how fast the speed of the truck is changing

5 miles per hour            1 second

10  miles per hour         2 seconds 

15 miles per hour          3 seconds

20 miles per hour          4 seconds

25 miles per hour           5 second

30  miles per hour         6 seconds 

35 miles per hour          7 seconds

40 miles per hour           8 seconds

45 miles per hour           9 second

50  miles per hour         10 seconds 

55 miles per hour          11 seconds

60 miles per hour          12 seconds

Every second, the speed of the truck increases or changes by 5 miles per hour.

You can see that the mustang increases its speed faster than the truck . We says that it has a greater acceleration and we can write:

15 m/h / 1 s
= 15 m/h.s

And this is where the definition of acceleration came from.

a =
change in speed / time interval

The 15 m/h.s is read as " 15 miles per hour-second

For the Mustang,

The change in speed is 30 - 15 = 15 or 45 - 30 = 15

The time interval is 2 - 1 = 1  or 3 - 2 = 1  etc.

When advertisers say that a car can go from 0 to 60 in 8 s, they are talking about the car acceleration, not the speed.

Expanding our definition of acceleration

It is not just a change in speed that causes acceleration.

Acceleration can also be caused by changing the direction of motion.

If the road curves, you will feel that your body is trying to move toward the outside of the curve. 

You are experiencing acceleration even if your speed is constant.

That is why the definition of acceleration is best described as the velocity divided by time.

Acceleration =
change in velocity / time interval

Acceleration just like velocity is directional. A change in either the speed, the direction, or both will cause acceleration.

Acceleration quiz

This acceleration quiz will clearly show the difference between speed and acceleration. You may need to use a paper and pencil to complete some of the questions.

My recommendation is to first read this lesson about the acceleration and then take this quiz without using a calculator.

Objective of the quiz:

  • Understand clearly what the acceleration is.
  • Apply the concept of acceleration to real life problems.
  • Identify the formula to use to find the acceleration.
  • Identify and understand the unit used for acceleration.
  • Identify the variables that can produce acceleration.

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