There are four equations, called the kinematic equations
that physicists use the analyze motion
whenever an object is moving with a constant acceleration:
The goal of this pod is to begin learning to use the first three of these equations.
Kinematic Equation 1: The Definition of Acceleration
$$
v_f = v_i + a \cdot \Delta t
$$

I have an initial velocity of 4 m/s.
I have an acceleration of 5 m/s^{2}.
I have a time of 4 seconds.
What is my final velocity?

I have an initial velocity of 18 m/s.
I have an acceleration of 2 m/s^{2}.
I have a time of 20 seconds.
What is my final velocity?

I have an acceleration of 3 m/s^{2}.
I have a time of 4 seconds.
I have a final velocity of 20 m/s.
What is my initial velocity?

I have an acceleration of 5 m/s^{2}.
I have a time of 3 seconds.
I have a final velocity of 40 m/s.
What is my initial velocity?

I have a final velocity of 30 m/s.
I have an initial velocity of 20 m/s.
I have a time of 5 seconds.
What is my acceleration?

I have a final velocity of 23 m/s.
I have an initial velocity of 5 m/s.
I have a time of 6 seconds.
What is my acceleration?
Kinematic Equation 2: The King of Kinematic Equations
$$
\Delta x = v_i \cdot \Delta t + \frac{1}{2}a \left( \Delta t \right)^2
$$
Note that I made this name up, because I think this is the most
important of kinematic equations. It isn't the official name. (But it should be!)

I have an initial velocity of 4 m/s.
I have a time of 3 s.
I hae an acceleration of 6 m/s.
What is my displacement?

I have an initial velocity of 5 m/s.
I have a time of 10 s.
I have an acceleration of 4 m/s^{2}.
What is my displacement?
Formula 3: The Average Speed Equation
$$
\Delta x = \left( \frac{v_i + v_f}{2} \right) \Delta t
$$

I have an initial velocity of 15 m/s.
I have a final velocity of 5 m/s.
I have a time of 3 seconds.
What is my displacement?

I have an initial velocity of 3 m/s.
I have a final velocity 13 m/s.
I have a time of 4 s.
What is my displacement?

I have an initial velocity 2 m/s.
I have a final velocity of 10 m/s.
I have a displacement of 48 m.
What was my time?

I have an initial velocity of 12 m/s.
I have a final velocity of 18 m/s.
I have a displacement of 90 m.
What was my time?