Episode 5 introduces the three kinematic equations and shares advice on the best way to use them. So grab your equations sheet and listen in! The episode begins with 5 rules and reminders (1:19). The three kinematic equations deal with 5 variables: acceleration, time, initial velocity, final velocity, and displacement. (2:11) When problem solving, write the variables in the same order and have the kinematic equations available. (6:37)
The Question of the Day asks:(8:34)
A negative acceleration means the object is a) Slowing down, b) depends on velocity direction or C) Speeding up
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INTRO: Hi and welcome to the APsolute Recap: Physics 1 Edition. Today’s episode will focus on the use of the kinematic equations and some tips for solving kinematics problems.
Lets Zoom out:
Unit 1 – Kinematics
Topic 1.1 – Position, velocity, and acceleration
Big Idea – Force Interactions
Motion can be described in three ways: through a narrative, with a graph, and using algebraic equations. Today we introduce the three kinematic equations, figure out the best way to use them, and how not to get lost in the sea of numbers.
Lets Zoom in:
Ok, so full disclosure… these equations are not magical number machines that let you take a jumble of numbers, toss them in, and the correct answers pop out. It does take a “getting to know you” period of time before most people master the use of these equations.
For these equations to be useful, you should be aware that:
A. the acceleration must be constant for the time period you are evaluating
B. the time we use in the equation is elapsed time
C. the normal rule about using matching units when calculating applies (you can’t use a miles per hour speed in a problem with a meter per second squared acceleration)
D. you need to select a starting location and stick with it throughout the problem, I usually let the starting location be the origin or 0 meters
E. pay very close attention to the directions of the vectors and use the appropriate mathematical signs.
Without further adieu … (**in a whisper** this would be a good time to pause and pull up the Physics 1 equation sheet)
Equation 1 defines acceleration.
In words, it says “the final velocity at the end of a time period in a given direction is equal to the initial velocity or the velocity at time zero seconds in that same direction added to the product of the time and acceleration in that direction.”
The “v’s” are for velocities, the “a” is for acceleration, and the “t” is for the elapsed time.
The subscript x’s mean traveling in the x-direction, so sometimes they are y’s when we are dealing in the vertical direction.
How can the equation be used? Well, say you over-confidently challenged a cheetah to a race, and you wanted to know how fast the cheetah was able to run, but you only knew that it started from rest, accelerates to its maximum velocity at a rate of 8.94 m/s2 and reached maximum velocity in just 3 seconds time… Then you could solve for the final velocity by multiplying the 8.94 m/s2 acceleration and the 3 s time to find that the cheetah’s max velocity is 26.8 m/s (which is 60 miles per hour).
Equation 2
In words, it says “the final position of an object is equal to the initial position at time 0 s plus the product of the initial speed of the object and the time plus the product of one half the acceleration and the time squared.” Three of the variables utilized were in Equation 1, while the newcomers are x, the final position and x0, the position at time 0 s. In fact - if you subtract the initial position from the final position, you actually have the displacement.
How can equation 2 be useful?
While competing on your high school’s robotics team, you are working on the code to get the robot to precisely cross the field. You know the robot can accelerate from rest at a rate of 4.7 m/s2 and you need to know how many seconds it will take the robot to get from its starting position to the ball 11 m away. With this equation you can find that it will take the robot 2.16 seconds.
The 3rd kinematic equation is
In words it says, the final velocity squared is equal to the initial velocity squared plus the product of two times the acceleration and the displacement in a given direction.
How can the third equation be useful? Ask any pilot! Imagine you are approaching the runway and you know the runway has 400 m of available asphalt and your plane can accelerate at a rate of -1.56 m/s2. How fast should you approach in order to safely land? Using this equation, you know a safe approach velocity is about 35 m/s.
An important item of note when solving for velocity vectors with the 3rd kinematic equation: you may need to use logic to determine the direction because of velocity being squared. This is where sketching a v-t graph can be very helpful.
With so many options of problems to solve and 3 options of equations to pick from, you may be wondering how can you keep all of this organized? It turns out, that any motion has 5 relevant features. List them in the same order when you solve any kinematic problems. I call this an a, t, v table and I list them in the order of acceleration, initial velocity, final velocity, time and displacement. Unfortunately, displacement doesn’t fit the acronym, but who’s counting! Listing the variables in the same order will help you to focus on the problem more and the amount of numbers floating around less.
Finally, have all three formulas available in one place. I find that along the top margin of my loose-leaf paper works well. This will allow you to see which equation will allow you to know 3 things and find 1 unknown quantity. If you solve for an unknown quantity that was not specifically asked for in the question, then at least you know more information about the scenario and are only missing the fifth quantity. The more you practice the better you will get. Physics is different from most subjects. Just reviewing problems you have already solved will usually not improve your ability to problem solve. You need to solve new problems, check the solutions, and if you are incorrect, look for why the solution differed from your answer. That’s it! The world is not short on problems, so let’s start solving them!
To recap……
There are 3 kinematic equations that can be found on the study guide and the Physics 1 formula sheet. In order to use these equations, the acceleration must be constant. These equations deal with 5 variables: acceleration, time, initial velocity, final velocity, and displacement. When problem solving, write the variables in the same order and have the kinematic equations available.
Coming up next on the APsolute RecAP Physics 1 Edition, we will turn 1-D on its side and look at objects in free-fall.
Today’s Question of the Day is about the direction of the acceleration.
Question: A negative acceleration means the object is…
Answer:
a) Slowing down
b) depends on velocity direction
c) Speeding up