Acceleration "a" is defined as the change in velocity "v" between two points 1 and 2 over time, "t." In mathematical notation, you express this relationship as:

**a = (v _{1} - v_{2})/t = ∆v/t**

If you can measure the velocity of an accelerating object at two different points along its path, but you don't have a way to measure time, you can still calculate acceleration. This works only if you can assume the acceleration is constant between points 1 and 2 and that the object travels in a straight line.

## Calculate the Average Velocity between Points 1 and 2

Average velocity is the sum of the velocities at point 1 and point 2 divided by 2:

**v _{av} = (v_{1} + v_{2})/2**

## Find the Time "t"

Velocity is defined as distance over time. Because you know the average velocity and the distance traveled, you can solve for "t":

** v_{av} = d/t**. Therefore,

*t = d/v*_{av}## Substitute for "t" in the Expression for Acceleration

The expression for acceleration is *a = (v _{1} - v_{2})/t*

Substituting *d/v*_{av} for ** t** and simplifying, we get:

**a= (v _{1} - v_{2})v_{av} /d**

## Example

A car accelerates uniformly for a distance of 1 mile on a straight road. At the beginning of the mile, it is traveling at a speed of 10 mph, and at the end, it's traveling at 80 mph. What is the acceleration, assuming it's constant?

First, find v_{av} = 10 + 80 / 2 = 45 mph.

Calling the end of the mile Point 1 and the beginning Point 2 to make the velocity difference a positive number, and using the expression that relates acceleration to velocity and distance, we get:

a = (80 - 10)45/1 = 1.56 miles/hour^{2}.