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Speed
To describe how fast an object moves, we use its speed. Speed is the distance an object travels per unit time.
We calculate speed by using the following:
| Speed equals distance divided by time. |
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The equation for speed is:
| s = d / t |
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The unit of measurement for speed is m/s, or meters per second. Sometimes speed is expressed:
- km/h or kilometer per hour
- mph or miles per hour (the English Standard)
Speed does not take into account the direction an object is traveling. Therefore, speed is a scalar quantitya quantity with magnitude but no direction.
Since speed is a scalar, it is described as having a magnitude and unit only. Magnitude is the number value. For example, Kyle rode his bike 5 m/s down the street.
- The "5" describes the magnitude.
- The m/s is the unit of measurement for speed.
Solving for Other Variables
This equation can be rewritten to solve for the total time or the total distance when the other two variables are known.
To solve for total time, we can rearrange the equation to read time equals distance divided by speed, or:
t = d / s
To solve for total distance, we can rearrange the equation to read distance equals speed multiplied by time, or:
d = s x t
Constant Speed
When an object is travelling at a constant speed, it does not speed up or slow down. The speed is the same regardless of the time interval chosen.
Most of the time, speed is not constant. For example, when you get in your car, you do not travel at the same speed the entire time. You speed up, then you slow down. You may stop and then speed up again. Because speed changes, we often talk about either average speed or instantaneous speed. We will look at both of these quantities in the next two sections of the lesson.
Average Speed
Average speed is the total distance traveled divided by the total time of travel. Average speed is calculated using the same formula as speed.
We denote average speed with the symbol savg, and we solve for average speed using the following:
| savg equals total distance (dT) divided by total time (tT) |
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The formula is written:
| savg = dT / tT |
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To find the total distance, or dT, you can add all of the distances traveled in a scenario.
To find the total time, or tT, you can add all of the time traveled.
Once you have these totals, you can divide the total distance by the total time to find the average speed of a particular journey.
Example
Let's try to solve for average speed in the following example. If a car travels 90 km in the first hour of a two-hour trip and then travels 110 km in the second hour, what is the car's average speed for the entire trip?
- First, let's identify the known values:
The first piece of information we're given indicates the car traveled a distance of 90 km in the first hour of the trip. From this information, we know:
- d1 = 90 km
- t1 = 1 h
The second piece of information we're given says the car traveled 110 km in the second hour of the trip. From this information, we know:
- d2 = 110 km
- t2 = 1 h
- Next, we need to combine the two distances traveled to find the total distance.
- d1 + d2= Total distance
- 90 km + 110 km = 200 km
- 200 km = Total distance
- Now we need to combine the two times to find the total time traveled.
- t1 + t2 = Total time
- 1 h + 1 h = 2 h
- 2 h = Total time
- Let's plug the total time and total distance into the average speed formula and solve.
- savg = dT / tT
- savg = 200 km / 2 h
- savg = 100 km/h
In this scenario, the average speed of the car was 100 km/h.
Instantaneous Speed
Instantaneous speed is how fast you are going at one point in time or one instant. A vehicle's speedometer shows instantaneous speed.
- If an object is speeding up or slowing down, its instantaneous speed is different at every point in time.
- When an object is moving with constant speed, the instantaneous speed does not change. The speed is the same at each point in time.
In general, there is no calculation for instantaneous speed since it is simply the speed at one specific point in time. It is reported simply using a magnitude and a unit. For example, the car was traveling at 6 m/s.