Compound Units

The basic units of measurement in the Metric System that we most frequently use in physics are the meter for length., the kilogram for mass, and the second for time. There is also the coulomb for electric charge and the Kelvin scale for temperature.

But there are many other quantities that we can measure in physics, such as force, velocity, electric current, magnetic field strength, etc. Using the basic units, we can construct units to attach to our measurements of these quantities.

We'll use velocity as our first example. A glance at the speedometer of a car indicates the units that we must use to measure velocity: miles per hour, or kilometers per hour. Both of these use terms of "distance per time." This is because velocity is the rate of change of position or distance over a period of time. Or, to put it in the form of an equation:

Velocity = Distance / Time

Using basic units, the physics unit for velocity are therefore meters per second, written in shorthand m/s. Most physics equations involving velocity will assume that the velocity is in m/s, so you will have to make sure that those are the units you are plugging in. Let's try an exercise in converting unitsof velocity:

The speed limit on a Canadian road is 110 km / hour. Given that 1 mile=1.61 kilometers, find the value of this speed limit in miles per hour. What is the speed in m/s?

110 kilometers /hour X (1 mile/1.61 kilometers) = 68.3 mi/hr

Note how, once again, we have arranged things such that the units of kilometers "cancel." Now to the second part:

110 kilometers /hour X (1000 meters/1 kilometers) = 110,000 m/hr

110,000 m/hr X (1 hour/3600 seconds) = 30.56 m/s

Note how we took things in two separate steps. It takes a little extra writing, but it's worth it to be accurate! Now for some more practice:

  1. How many m/s is 70 miles per hour?

  2. Light travels at 300,000 km/s. What is that speed in m/s and mi/hr?

  3. It takes you 4 hours to travel 200 miles. On average, how fast were you driving, in mi/hr and in m/s?

Now move on to check your answers and find out about some more compound units.

Questions? Ask the designer, Jim Heath

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