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AP Physics 1: Exam Prep13 chapters | 143 lessons | 6 flashcard sets

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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.

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.

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.

These are the Big Five Equations:

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

The symbol delta (Î”) 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.

There's one more point to make here. In some questions, it may seem you are missing key information, specifically initial position. If you're looking for a change in position over a period of time and the question doesn't give you an initial position, you can assume it is 0 meters. Remember to always double-check your variables and your equations and be very careful assuming anything.

Let's work through a typical problem so you get an idea of how to tackle them.

*A race car sitting on the start line of a straight track accelerates uniformly for 3.6 seconds at a rate of 4.5 m/s^2. If the initial velocity is 0 m/s, how far does the car travel during this time interval?*

First, let's write down the variables we're given in the equation.

*t* = 3.6 s*a* = 4.5 m/s^2*v* sub 0 = 0 m/s*x* sub 0 = 0 m. This isn't given, but you can assume it is 0 m in order to calculate the change in position.*x* = what the problem is asking you to solve for.

Now, look at the Big Five Equations. Only one will have exactly these five variables. In this case, we need Equation 3: *x* = *x* sub 0 + *v* sub 0**t* + ½ *at*^2. Now, start filling in the blanks and calculate the answer.

So, in this problem, the racer travels about 29 meters in 3.6 seconds. You must include the units, which is meters.

If at any point during questions like this, you are unsure if you have the right equation, try plugging the numbers into multiple equations. You'll quickly find out that you have unused values or the equation needs a value you don't have.

Let's briefly review.

In order to get more comfortable solving problems with different combinations of position, displacement, velocity, and acceleration variables, we simplify a couple aspects of these problems. First, we assume that all acceleration is uniform, meaning it occurs at the same rate from start to finish. Second, we only look at motion in a straight line, so the direction associated with vector quantities is positive or negative only.

There are five equations you need to memorize for solving uniformly accelerated motion problems. The best way to get started is to identify all the variables, including the one you need to calculate, and look for the equation that has all of them. Then simply plug them in and do the math. Remember, in order to get the question right, you need to include the proper units.

Once you have completed this lesson, you should be able to:

- Recall the Big 5 equations for uniformly accelerated motion
- Identify the variables in a uniformly accelerated motion equation
- Solve a uniformly accelerated motion problem

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AP Physics 1: Exam Prep13 chapters | 143 lessons | 6 flashcard sets

- What is Kinematics? - Studying the Motion of Objects 3:29
- Scalars and Vectors: Definition and Difference 3:23
- What is Position in Physics? - Definition & Examples 4:42
- Distance and Displacement in Physics: Definition and Examples 5:26
- Speed and Velocity: Difference and Examples 7:31
- Acceleration: Definition, Equation and Examples 6:21
- Significant Figures and Scientific Notation 10:12
- Uniformly-Accelerated Motion and the Big Five Kinematics Equations 6:51
- Ticker Tape Diagrams: Analyzing Motion and Acceleration 4:36
- What are Vector Diagrams? - Definition and Uses 4:20
- Using Position vs. Time Graphs to Describe Motion 4:35
- Determining Slope for Position vs. Time Graphs 6:48
- Using Velocity vs. Time Graphs to Describe Motion 4:52
- Determining Acceleration Using the Slope of a Velocity vs. Time Graph 5:07
- Velocity vs. Time: Determining Displacement of an Object 4:22
- Understanding Graphs of Motion: Giving Qualitative Descriptions 5:35
- Free Fall Physics Practice Problems 8:16
- Graphing Free Fall Motion: Showing Acceleration 5:24
- The Acceleration of Gravity: Definition & Formula 6:06
- Projectile Motion: Definition and Examples 4:58
- Projectile Motion Practice Problems 9:59
- Kinematic Equations List: Calculating Motion 5:41
- Go to AP Physics 1: Kinematics

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