Practice Applying Velocity & Energy Formulas

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Velocity and energy problems are common in physics. In this lesson we will learn how to calculate velocity and kinetic/potential energy and go through some practice problems.

Energy

We often talk about energy in our day to day life. It can be the energy that we do or do not have. Or the energy used to power our homes and cars. But what is energy? One way to describe energy is by describing the movement that an object is experiencing or will experience. Using this explanation of energy it makes sense that formula for calculating kinetic energy uses velocity, or speed. Kinetic energy can be defined as the energy an object has due to the movement of that object.

So in order to calculate energy we need to know the velocity of an object.

Velocity Calculations

Velocity is how quickly (in seconds, minutes, or hours) we travel a set distance (in meters, miles, or feet). In order to calculate velocity we take the change in distance (x) divided by the change in time (t):


Velocity formula


Let's say that you were driving to your friend's house. You started at 9:30 and you got there at 9:50. And you know that it is 15 miles away. What is the average velocity you were driving?


velocity calculation


So, you were driving 50 miles per hour (mph) on average.

Now let's look at this equation a little differently. Let's say that you know that the speed limit on the freeway is 75 mph, and you tend to go the speed limit on average. You have another 50 miles before your exit. How long will it take you to get to your exit?

In order to solve this equation we need to rearrange the formula a little bit:


time formula


Now we can plug in the information that we have:


time to exit


It will take 40 minutes to get to your exit.

Kinetic Energy

Now that we know how to calculate velocity we can better understand how to calculate Kinetic Energy problems. The formula for kinetic energy (KE) is one half of mass (m) times velocity (v) squared:


Kinetic Energy formula


Typically kinetic energy is measured in joules (J) which is equal to one kilogram times one meter squared divided by one second squared:


Joule units


This tells us that we need our units to be in kilograms and meters. If the mass is not in kilograms be sure to convert it to kilograms. And be sure to convert velocity into meters per second (m/s).

Now let's take the example above, with the car, and determine the kinetic energy of the car driving down the freeway. It is going 75 mph which equals 34 m/s and the average weight of a car is about 1800 kilograms.


Kinetic energy calculated


So, the kinetic energy of this car is 1.0 mJ (a megajoule, mJ, is equal to one million joules).

Potential Energy

Another type of energy is called potential energy, or the energy due to the position of an object. The best way to think about potential energy is to think about you holding a rock out of a the window of a large skyscraper. If you dropped that rock it would fall (kinetic energy) but currently it isn't moving. Since energy is never created or destroyed, where does that kinetic energy come from. Before the rock is dropped it is in the form of potential energy.

Potential energy (PE) is equal to the mass (m) of the object times acceleration due to gravity (g) times the height (h) of the object.


Potential energy formula


If the rock in the above example has a mass of 2.3 kg, the window in the skyscraper is 550 meters from the ground, and we know that acceleration due to gravity is 9.8 m/s^2, then we can calculate the potential energy:


Potential energy calculation


The potential energy of this rock is 12 kJ (a kilojoule, kJ, is equal to 1000 joules).

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