Solving Kinematics Problems

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  • 0:04 Kinematics
  • 0:56 The Kinematics Equations
  • 1:58 Using a Kinematics Equation
  • 4:26 Lesson Summary
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Lesson Transcript
Instructor: Christopher Muscato

Chris has a master's degree in history and teaches at the University of Northern Colorado.

How do we use physics to answer questions about motion? One way is with kinematics, and in this lesson we'll examine several kinematics equations and how to use them.


Do you ever feel like the world is spinning out of control, like the constant motion of life could just overwhelm you at any moment? Well, I can't do anything to help you with that, but we can talk about some neat equations to calculate motion.

In physics, one of the major areas of focus is classical mechanics, the study of the motion of objects, as first described by good old Sir Isaac Newton himself. So, we are studying motion, the impact of force upon a body at rest, etc. There are several ways we could do this, with charts, or pictures, or whatnot, but today, we'll focus on kinematics, the study of motion through equations. Some people call this the geometry of motion. Basically, we are going to break down the motion of an object into variables that can be calculated through geometric formulas. But don't worry, you can stay sitting down for this. As Newton says, 'a body at rest, should stay at rest.'

The Kinematics Equations

Alright, so kinematics is the study of motion through equations. What are these equations? There are actually four standard kinematics equations that are generally used to resolve questions of motion. These are them:

d = vi * t + ½ * a * t^2

vf^2 = vi^2 + 2 * a * d

vf = vi + a * t

d = '(vf + vi) / 2) * t

So what are we looking at? These equations are used to calculate unknown information about an objects motion in respect to known variables. In general, as long as you know three of the variables, you can figure out the fourth. They are:

  • d for displacement of object, which is basically the distance it moves
  • t for time object was moving
  • a for acceleration
  • v for velocity

Actually, we can break this last one up into vi, for initial velocity, and vf, for final velocity.

So, if we look at one of these equations - say this one (vf = vi + a * t) - what it really says is final velocity equals initial velocity plus acceleration times time. Times, time! Anyway, as long as you know three of the variables, you can figure out the fourth.

Using a Kinematics Equation

OK, so let's see this in action. Say that we are driving along, la-dee-dah. Now say that I start speeding. I'm pushing 80 mi/hr, going over the speed limit, and we zip past a parked cop car, who turns on his lights and starts chasing us. Now, if he wants to catch up to us in about 10 seconds, how fast does he need to accelerate? Well, let's use kinematics. The first step to solving a kinematics equation is to figure out what you know and what you don't know. So let's go through our variables.

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