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# Average Acceleration

## Define and calculate average acceleration using formulas

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Average Acceleration

To escape from Earth's orbit, space shuttles such as the Atlantis shown here must accelerate to 28,968 kilometers per hour, called the shuttle's escape velocity.

### Average Acceleration

An object whose velocity is changing is said to be accelerating.  Average acceleration, a¯\begin{align*}\overline{a}\end{align*} is defined as the rate of change of velocity, or the change in velocity per unit time. The units of acceleration are distance over time squared. A symbol with a bar over it is read as average – so a-bar is average acceleration.

Example:  A car accelerates along a straight road from rest to 60. km/h in 5.0 s. What is the magnitude of its average acceleration?

Solution:

The acceleration in this problem is read as kilometers per hour per second.  In general, it is undesirable to have two different units for the same quantity in a unit expression. In this case, it is undesirable to have both hours and seconds. To eliminate this problem, we convert the hour units to seconds. Converting the original 60. km/h to m/s, gives 17 m/s.

17m/s5s=3.4m/s2\begin{align*}\frac{17m/s}{5s}=3.4m/s^2\end{align*}

The acceleration is 3.4 m/s2.

Example:  An automobile is moving along a straight highway in the positive direction and the driver steps on the brakes. If the initial velocity is 15.0 m/s and 5.0 s is required to slow down to 5.0 m/s, what was the car’s acceleration?

Solution:

a¯=ΔvΔt=10. m/s5.0 s=2.0 m/s/s\begin{align*}\overline{a} = \frac{\Delta v}{\Delta t} = \frac{-10. \ \text{m/s}}{5.0 \ \text{s}} = -2.0 \ \text{m/s/s}\end{align*}

Note that an acceleration is merely a change in velocity. This change can be either positive or negative. A negative change, such as that in the example problem above, is sometimes called negative acceleration or deceleration.

#### Summary

• Average acceleration is the rate of change of velocity, or the change in velocity per unit time.

#### Practice

Complete the activity found at this URL to help you understand acceleration.

Review

1. The velocity of a car increases from +2.0 m/s to +16.0 m/s in a time period of 3.5 s.  What was the average acceleration?
2. If an automobile slows from +26 m/s to +18 m/s in a period of 4.0 s, what was the average acceleration?
3. If a runner increases his velocity from 0 m/s to +20 m/s in 2.0 s, what was his average acceleration?
4. If a runner decreases his velocity from +20 m/s to +10 m/s in 2.0 s, what was his average acceleration?