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### 302-C: Kinematic Equations 1: Kinematic Equations with Information Given

• Topic Cluster: Kinematics
• Topic: Forward Kinematics Quantitative
• Objective: Solve 1-2 step numerical algebraic problems with the kinematic equations with equations and information given.
• Content: The four kinematic equations relate the five kinematic variables for an object moving with a constant acceleration.
• Level: 2

#### BACK to Ladder Forward Kinematics Quantitative

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

$$v_f = v_i + a \cdot \Delta t$$

1. I have an initial velocity of 4 m/s.
I have an acceleration of 5 m/s2.
I have a time of 4 seconds.
What is my final velocity?
2. I have an initial velocity of 18 m/s.
I have an acceleration of 2 m/s2.
I have a time of 20 seconds.
What is my final velocity?
3. I have an acceleration of 3 m/s2.
I have a time of 4 seconds.
I have a final velocity of 20 m/s.
What is my initial velocity?
4. I have an acceleration of 5 m/s2.
I have a time of 3 seconds.
I have a final velocity of 40 m/s.
What is my initial velocity?
5. 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?
6. 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!)

1. 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?
2. I have an initial velocity of 5 m/s.
I have a time of 10 s.
I have an acceleration of 4 m/s2.
What is my displacement?

### Formula 3: The Average Speed Equation

$$\Delta x = \left( \frac{v_i + v_f}{2} \right) \Delta t$$

1. 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?
2. 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?
3. 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?
4. 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?