Kinematic Formulas: 4 Things You Should Know About Them

When solving a physics problem, the first step is always to identify all given information and what unknown information needs to be found. This includes considering if there are more unknown variables than known variables or vice versa.  A set of kinematic formulas exist for you to solve physics problems. Have you ever wondered what they look like or how to use them? This article covers those questions and more.

The Key Formulas 

When solving this type of equation, the formulas are essential. When you do your research by reading this article or other similar articles online, you’ll know that this is the key. Here are some illustrations for better understanding. 

          vf^2 = vi^2 + 2ad

                distance = rate x time

                displacement = final velocity – initial velocity

                acceleration = change in velocity/time period of motion

After being given a set of variables, you can use these four kinematic formulas to solve for the unknown variable. Here is an example that will help you visualize how to use them:

Example problem: A ball is thrown with a velocity of 20 m/s from the top of a building which is 35m tall. How long does it take for the ball to hit the ground?

In this example, you have been given your starting velocity, the distance from the top of the building to where it lands, and how long it takes.

You can use these three equations to solve for time:

a = -9.8 m/s^2*35m = 269.4 s^-2 * 35m

t = (20 m/s) * (35m) /(-9.8 m/s^2*35m)

t = 3.26 seconds

This is because the acceleration due to gravity, -9.8 m/s^2, cancels out and doesn’t appear in the final answer as long as you use the gravitational acceleration (g) for your calculation.

                vf^2 = vi^2 + 2ad

                20m/s * 20 m/s = 10 m/s^2* 35m

                269.4 s^-2 * 35m / (10 m/s^2*35m)

                269.4 s^-2 * 35m = 3645.832 m

                9.8 m/s^2 * 35m / 269.4 s^-2 * 2

                t = 3.26 seconds

If you don’t know the distance, you could also use the first equation to solve for it.

vf^2 = vi^2 + 2ad

20m/s * 20 m/s = 10 m / s^2*35m 

(20m/s) * 35m = 21 m / s^2 * 35m

t = (vf^2 – vi^2) / (2ad)

t = (10 m/s^2 * 35m – 20 m/s ^ 2) /(-5 m/s^2* 35m)

t = 3.26 seconds

Use The Kinematic Formulas In Reverse

Be careful when solving for your known variables. You don’t want to accidentally solve the incorrect equation! If it’s too time-consuming or difficult to calculate, draw a free-body diagram that will help you visualize the problem and the four key kinematic equations.

  • detail the path the object travels
  • calculate horizontal momentum gained during each time interval
  • use horizontal force diagrams to find impulse and change in kinetic energy for each section of the object’s travel

This approach requires a lot of careful thought and attention, but you’ll come away with a complete picture of what is going on. Using this approach to solve for an unknown variable will make it much easier.

Kinematic Equations Don’t Care About Your Problem’s Units

Math matters when you’re solving physics problems, but not to the degree that many students believe. In fact, you can solve for any unit of measure if you know the right formula to use and have all of the information that the problem requires.

solve for “t,” your time in seconds after a number is in front of it in a kinematic equation, you can convert to any other unit of measure in order to solve for time if necessary. For example:

Converting from one unit of measure to another certainly helps when solving physics problems, but you have to be aware of the relationship between them. For example, if “v” represents miles per hour in one equation and meters per second in another, they are not equivalent. This means you can’t solve for unknowns in these problems without converting the units first.

Kinematic Equations Are Used For More Than Solving For Time

The kinematic equations are used to solve for the unknown variable in any problem where velocity, acceleration, or distance is given. You can use these formulae to solve for anything, including position, height above ground level, final velocity, average velocity during a certain interval of motion.

In conclusion, the 4 things you should know about kinematic equations are to use them in reverse, don’t care about your problem’s units, they can solve for anything if given enough information like velocity, acceleration, or distance and that all of the four key kinematic equations contain time in seconds.