# 4.4: Speed

Difficulty Level: At Grade Created by: CK-12
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Did you ever play fast-pitch softball? If you did, then you probably have some idea of how fast the pitcher throws the ball. For a female athlete like the one in the opening image, the ball may reach a speed of 120 km/h (about 75 mi/h). For a male athlete, the ball may travel even faster. A fast-pitch pitcher uses a “windmill” motion to throw the ball. This is a different technique than other softball pitches, and it explains why the ball travels so fast.

### Introducing Speed

How fast or slow something moves is its speed. Speed determines how far something travels in a given amount of time. The SI unit for speed is meters per second (m/s). Speed may be constant, but often it varies from moment to moment.

### Average Speed

Even if speed varies during the course of a trip, it’s easy to calculate the average speed by using this formula:

speed=distancetime\begin{align*} speed=\frac{distance}{time}\\\end{align*}

For example, assume you go on a car trip with your family. The total distance you travel is 120 miles, and it takes 3 hours to travel that far. The average speed for the trip is:

speed=120mi3h=40mi/h\begin{align*} speed=\frac{120mi}{3h}\\=40mi/h\end{align*}

Q: Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri ¼ hour to make the round trip. What was her average speed for the entire trip? (Hint: The round-trip distance is 6 km.)

A: Terri’s speed can be calculated as follows:

speed=6km0.25h=24km/h\begin{align*} speed=\frac{6km}{0.25 h}\\=24km/h\end{align*}

### Instantaneous Speed

When you travel by car, you usually don’t move at a constant speed. Instead you go faster or slower depending on speed limits, traffic lights, the number of vehicles on the road, and other factors. For example, you might travel 65 miles per hour on a highway but only 20 miles per hour on a city street (see the pictures in the Figure below.) You might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars. Therefore, your speed at any given instant, or your instantaneous speed, may be very different than your speed at other times. Instantaneous speed is much more difficult to calculate than average speed. If you want to learn more about calculating speed, watch the video at this URL:

Cars race by in a blur of motion on an open highway but crawl at a snail’s pace when they hit city traffic.

### Calculating Distance or Time from Speed

If you know the average speed of a moving object, you can calculate the distance it will travel in a given period of time or the time it will take to travel a given distance. To calculate distance from speed and time, use this version of the average speed formula given above:

distance = speed x time

For example, if a car travels at an average speed of 60 km/h for 5 hours, then the distance it travels is:

distance = 60 km/h x 5 h = 300 km

To calculate time from speed and distance, use this version of the formula:

time=distancespeed\begin{align*} time=\frac{distance}{speed}\\\end{align*}

Q: If you walk 6 km at an average speed of 3 km/h, how much time does it take?

A: Use the formula for time as follows:

time=distancespeed=6km3km/h=2h\begin{align*} time=\frac{distance}{speed}\\=\frac{6km}{3km/h}\\=2h\end{align*}

### Summary

• How fast or slow something moves is its speed. The SI unit for speed is meters per second (m/s).
• Average speed is calculated with this formula: speed=distancetime\begin{align*}speed=\frac{distance}{time}\\\end{align*}
• Speed may be constant, but often it varies from moment to moment. Speed at any given instant is called instantaneous speed. It is much more difficult to calculate than average speed.
• Distance or time can be calculated by solving the average speed formula for distance or time.

### Vocabulary

• speed: How quickly or slowly something moves; calculated as distance divided by time.

### Practice

Do problems 1–3 on the average speed worksheet at the following URL.

### Review

1. What is speed?
2. If you walk 3 kilometers in 30 minutes, what is your average speed in kilometers per hour?
3. Compare and contrast instantaneous and average speed.
4. What distance will a truck travel in 3 hours at an average speed of 50 miles per hour?

### Notes/Highlights Having trouble? Report an issue.

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### Vocabulary Language: English

TermDefinition
speed How quickly or slowly something moves; calculated as distance divided by time.

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