The Kinematics Equations
of Motion
(for constantly accelerated, straight-line motion)
These equations may seem a little bit overwhelming at first, but they
really aren’t that bad once you get to know them, and they really are
powerful! With them, you will be able to solve just about any motion
problem we encounter this year. We will use them over and over
again throughout the course, so it is in your best interest to get to
know them very well (& keep this sheet handy)!
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Equations
Missing
Variable
v f = vi + a(Δt)
x
Δx = vi (Δt) + 21 a(Δt)2
vf
v2f = v2i + 2a(Δx)
t
Δx = 21 (vi + v f )Δt
*this formula is NOT on the MCAS formula sheet, but
v avg =
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vi + v f
2
a
is…
What do all those variables stand for???
Δx = displacement
vi = initial velocity
vf = final velocity
Δt = time interval
a = acceleration (needs to be constant, can be zero)
Solving Problems Using the
Kinematics Equations of
Motion
1. Define Variables:
(Include
Units!)
vi =
Make a labeled diagram in
the space below.
vf =
Δx =
a=
t=
2. Plan Make a prediction. What type of answer do you expect? What will the
units be? How big or how small will the number be? Will it be close to onemillion, one-thousand, one-hundred, one, or one-hundreth?
Prediction:
Choose your equation. Hint: Figure out which variable is not being
used (as an unknown or a known), and use the Kinematics Equation that
does not use that variable.
Equation:
3. Calculate Substitute the values into the equation and solve. Now you
can start to work with the numbers. Some people like to solve the equation
algebraically for the unknown variable first and then plug in numbers, while
others like to plug in the numbers and then solve. This is up to you.
4. Evaluate Ask yourself the following: Does the answer make sense?
Do you end up with a numerical (number) close to what you
expected, or is it way off? Do you end up with the appropriate units? Do
you end up with the appropriate sign (positive or negative)?