Uniformly-Accelerated Motion and the Big Five Kinematics Equations

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  • 0:01 Lead with a Physics Joke
  • 0:59 Uniformly Accelerated Motion
  • 2:11 The Big Five Equations
  • 4:08 Putting the Equations to Work
  • 6:02 Lesson Summary
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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

In this lesson, we will begin to solve problems that combine position, displacement, velocity, and acceleration. I will introduce the Big Five Equations to help you on your way.

Lead with a Physics Joke

There's a joke in the physics world that goes something like this:

A farmer calls in a biologist, a chemist, and a physicist to help him figure out what's wrong with his sick chickens. The biologist examines them but can't formulate a hypothesis to explain the illness. The chemist runs some tests, but his results are inconclusive. The physicist just looks at the chickens for a long time, scribbles down some notes, and announces that he has found the cure, but it only works for spherical chickens at zero kelvin in a vacuum.

The dig in this joke is that the world of physics has so many possible variables that attempting to create accurate models and relationships between them can be a nightmare, if not totally impossible. That's why we have to simplify things. By first only looking at the frozen, vacuumed, spherical chickens, we can make predictions on how they should behave. These simplified predictions can later be expanded to include more and more variables as the budding physicist gains more and more knowledge.

Uniformly Accelerated Motion

In order to get more comfortable working with kinematics, we're going to use this tactic as well. At this point, you should be comfortable solving problems involving position, displacement, velocity, and acceleration on their own. So we're going to take it a step further and combine them. But we need to simplify a couple things.

First, we'll only look at objects that are accelerating at a constant rate, called 'uniformly accelerated motion.' This is rarely achieved in the real world due to additional outside forces creating variability in how fast or slow an object accelerates through its entire motion. To make it easier, we're not going to bother with any of those yet.

Second, we'll only look at objects traveling in a straight line. This eliminates any messy issues with the directional component required for vector quantities and calculations. Since we're stuck on one straight line, the only directions we need to worry about are forwards and backwards, which we'll call positive and negative. For these problems, the sign is enough. No additional descriptors like north, up, or left are needed.

These limitations might seem unrealistic in the real world, but uniformly accelerated motion in a straight line is a great way to learn how the kinematics concepts fit together into five basic equations.

The Big Five Equations

These are the Big Five Equations:


big five


As a quick refresher, first I'll define each of the variables.

The symbol delta (Δ) means 'a change in.'

x = final position

x sub 0 = initial position

v = final velocity

v sub 0 = initial velocity

v with a bar over it = average velocity

a = acceleration

t = time

Uniformly accelerated motion questions will provide you with some of these pieces of information and ask you to solve for an unknown quantity. The key is to pull out the values and identify which ones you have, which you need to determine, and which are not included in the question at all. Then, simply plug them into the proper equation. This might sound like easy 'fill-in-the-blanks and do the math,' but it can be a bit more complicated than that. I'm sorry, but you have to memorize these five equations. None of the multiple choice questions you encounter will provide them for you.

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