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NY Regents Exam - Physics: Test Prep & Practice12 chapters | 132 lessons | 7 flashcard sets

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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.'

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:

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

Actually, we can break this last one up into ** vi**, for initial velocity, and

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.

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.

- Do we know the distance he would have to travel to catch us? No.
*d*= ? - How about the time? Well, yeah, we know he wants to catch us in 10 seconds, so
.*t*= 10 - Acceleration? Well, that's what we are trying to figure out, so again,
*a*= ? - How about the velocities? He was parked, so initial velocity, or
, and he wants to catch us while we are doing 80, so final velocity, or*vi*= 0.*vf*= 80

So, do we have three known variables? Yes, we know time, initial velocity, and final velocity.

The next step is to figure out which equation to use. To do this, you just look for the equation that can hold the three known variables and the unknown variable you want to figure out. The first two require both distance and acceleration, so that won't work, since we have two unknowns. Here we go:

*vf* = *vi* + *a* * *t*

We know three of these variables and have one unknown - acceleration. Now we plug it in so it looks like this:

**80 = 0 + ( a * 10)**

And we solve it. That becomes:

80 mi/hr = *a* * 10 s

80 mi/hr / 10 s = *a*

8 mi/hr/s = *a*

So *a*, or acceleration, is 8 mi/hr/s - not the usual units, but it makes sense if you think about it. So if this cop accelerates for 10 seconds, he'll need to gain 8 mi/hr of speed per second to catch us. We can check this by plugging *a* back into the original equation, making it:

80 = 0 + 8 * 10

80 = 80

Yep, that checks out. Ok, next problem: figure out how fast we need to go in order to get out of here to avoid the cop. Andâ€¦go!

When you feel like life is spinning out of motion, don't panic - just calculate. In **classical mechanics**, the study of the motion of objects, we can look at how objects move between rest and motion in various ways. One of those ways is **kinematics**, the study of motion through equations. There are four standard kinematics equations generally used to resolve questions of motion. To solve these equations, you need three known variables and one unknown variable. That's the first step to solving a kinematics problem: identifying your known and unknown variables. Then you find the equation that fits those variables and solve for the one unknown. With a knowledge of kinematics, you can get your body out of rest and set your physics career in motion.

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NY Regents Exam - Physics: Test Prep & Practice12 chapters | 132 lessons | 7 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
- Uniformly-Accelerated Motion and the Big Five Kinematics Equations 6:51
- Representing Kinematics with Graphs 3:11
- 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
- Solving Kinematics Problems 5:16
- Go to Kinematics Principles

- Go to Mechanics

- Go to Magnetism

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