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

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

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?

    BACK to Ladder Forward Kinematics Quantitative

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