Kinematic Equations made easy

David O’DellAnderson High School

What we should already know

• V = xf - xi / t• Velocity is change in position divided by time• a = vf – vi / t• Acceleration is change in velocity divided by

time

What if we wanted to know the future?

• Exactly where an object would land on the ground if I threw it far away?

• What the maximum height might be if I launched some fireworks into the air?

• Whether or not an airplane could safely land on a short runway?

What if we wanted to know the past?

• Was a driver under the speed limit when they were in a car that skidded 100 feet into a tree?

• Exactly how far away a sniper was when he shot a target.

• From exactly which floor of the Empire State building a penny fell and hit some poor soul on the head.

We can, with these:

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

What are the variables?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

• v or sometimes Vf stands for final velocity• v0 or sometimes Vi stands for initial velocity• a stands for acceleration• t stands for time

What are the variables?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

• x or sometimes xf stands for final position• x0 or sometimes xi stands for initial position•Sometimes the letter ‘s’ is used for position

What are the variables?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

How would you BEST use them?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

• good for figuring out how fast something was going (initial velocity), or will end up going (final velocity) if you have the acceleration and time.

• Also good for figuring out how much time it takes for something to reach a certain speed like an aircraft lifting off or a race car starting from rest.

How would you BEST use them?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

• Figuring out how far an object moved when it decelerated when knowing velocity, time and acceleration• Figuring out the initial velocity of an object knowing the distance it traveled (whether or not a driver was over the speed limit)

How would you BEST use them?

212

2 20 2 ( )

o

o o

v v at

x x v t at

v v a x

• How fast something will go given enough distance to travel

•How far something will travel if you only know the speeds and acceleration (don’t know the amount of time)

Let’s review some common relationships

• Situation:– An airplane is speeding up about to take off from a runway. – If the plane for some reason needs more time to take off,

perhaps it is fully loaded and going slower than usual, what can you say about the runway distance it will need?

• Obviously the runway will need to be longer. The distance it travels will be increased because it’s traveling slower. So…

• Distance depends on speed, time and how fast the plane can accelerate.

Let’s review some common relationships

• Situation:– a ball is dropped from rest from a height of 10 meters

(about 30 feet). Gravity is the only force acting on it.– If we drop the ball from a higher vertical position, say,

20 meters, what can we say about the time it takes to hit the ground?

• Of course it will take more time to hit the ground because it has more distance to travel. So…

• Time falling depends on height and the strength of gravity

Let’s review some common relationships

• Situation:– Skid marks are found at a car crash, they are 100

meters long. – If the driver had been driving the speed limit, the

skid marks for that model of vehicle would have been 60 meters.

• The amount of distance it takes to come to a full stop depends on the strength of deceleration, and the initial velocity.

Let’s review some common relationships

• Situation:– Skid marks are found at a car crash, they are 100

meters long. – If the driver had been driving the speed limit, the

skid marks for that model of vehicle would have been 60 meters.

• The amount of distance it takes to come to a full stop depends on the strength of deceleration, and the initial velocity.

How powerful are these?

• Extremely powerful, and used all the time:• A new runway was built on a small island that is 800

meters long. They want to extend the runway to handle bigger airplanes.

• How many more meters must the extension be in order to allow the 777 to land safely and not kill the passengers when only given:

• Plane’s initial velocity is 100 m/s upon touch down• Plane’s deceleration is -5 m/s/s• Final velocity is 0 m/s, it comes to a full stop

Solution

• Plane’s initial velocity is 100 m/s upon touch down• Plane’s deceleration is -5 m/s/s• Final velocity is 0 m/s• I need to find distance, is there an equation that helps

me find distance knowing those three variables?• YES. Vf

2 = Vi2 + 2ad

• Simply solve for ‘d’• d = 1000 meters. So the plane needs another 200

meters to land safely.

• http://dev.physicslab.org/Document.aspx?doctype=5&filename=Kinematics_KinematicsEquations1.xml