How to Calculate Centripetal Acceleration of an Orbiting Object
How to Calculate Power Based on Work and Time
How to Calculate Work That Is Opposite the Direction of an Object’s Motion

How to Calculate Power Based on Force and Speed

In physics, you can calculate power based on force and speed. Because work equals force times distance, you can write the equation for power the following way, assuming that the force acts along the direction of travel:

image0.png

where s is the distance traveled. However, the object’s speed, v, is just s divided by t, so the equation breaks down to

image1.png

That’s an interesting result — power equals force times speed? Yep, that’s what it says. However, because you often have to account for acceleration when you apply a force, you usually write the equation in terms of average power and average speed:

image2.png

Here’s an example. Suppose your brother got himself a snappy new car. You think it’s kind of small, but he claims it has over 100 horsepower. “Okay,” you say, getting out your clipboard. “Let’s put it to the test.”

Your brother’s car has a mass of

image3.png

On the big Physics Test Track on the edge of town, you measure its acceleration as 4.60 meters/second2 over 5.00 seconds when the car started from rest. How much horsepower is that?

You know that

image4.png

so all you need to calculate is the average speed and the net applied force. Take the net force first. You know that F = ma, so you can plug in the values to get

image5.png

Okay, so the force applied to accelerate the car steadily is 5,060 newtons. Now all you need is the average speed. Say the starting speed was vi and the ending speed vf . You know that vi = 0 m/s, so what is vf? Well, you also know that because the acceleration was constant, the following equation is true:

vf = vi + at

As it happens, you know that acceleration and the time the car was
accelerated over:

vf = 0 m/s + (4.60 m/s2)(5.00 s) = 23.0 m/s

Because the acceleration was constant, the average speed is

image6.png

Because vi = 0 m/s, this breaks down to

image7.png

Plugging in the numbers gives you the average velocity:

image8.png

Great — now you know the force applied and the average speed. You can use the equation

image9.png

to find the average power. In particular

image10.png

You still need to convert to horsepower. One horsepower = 745.7 watts, so

image11.png

Therefore, the car developed an average of 78.0 horsepower, not 100 horsepower. “Rats,” says your brother. “I demand a recount.”

Okay, so you agree to calculate power another way. You know you can also calculate average power as work divided by time:

image12.png

And the work done by the car is the difference in the beginning and ending kinetic energies:

W = KEfKEi

The car started at rest, so KEi = 0 J. That leaves only the final kinetic energy to calculate:

image13.png

Plugging in the numbers gives you:

image14.png

So because

image15.png

and the work done was

image16.png

you get the following:

image17.png

And, as before

image18.png

“Double rats,” your brother says.

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Calculating the Acceleration of an Object in Simple Harmonic Motion
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