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Kinematic Equations
Key point
- The four fundamental kinematic equations can be used to solve for the basic kinematic quantities of almost every motion problem
Defining Variables:
- u is the initial velocity.
- v is the final velocity.
- a is acceleration.
- t is time.
- s is displacement
- The i subscript is for initial; f for final.
In most kinematics problems, you will be tasked with finding the value of one of these variables with the equations below.
- More complex scenarios ask you to find more than one of these variables.
Formula Booklet
- This equation uses the final velocity given the initial velocity, the acceleration, and the time interval
- Often the initial velocity is 0.
- Derivation of the equation
- The area under a velocity vs. time graph is the change in position (displacement)
- The gradient of a velocity vs. time graph is its acceleration.
- The y-intercept is the initial velocity.
Formula Booklet
- Solving for the area of the velocity vs. time graph we get following equation:
- Remember that the initial displacement is often 0
- Notice how acceleration is not needed for this equation
- Use whenever acceleration is not given.
- Through combining the first two formulas and some basic algebra we get following formula:
- Remember that the initial velocity is often 0
- Notice how final velocity is not needed for this equation.
- Use when final velocity is not given.
Formula Booklet
Formula Booklet
- Through combining the first two formulas and some basic algebra we get following formula:
- Remember that the initial velocity is often 0
- Notice how time is not needed for this equation
- Use when time is not given.
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