Literal Equations
(Rearranging Equations)
Warm Up 9-13
1)
An airplane starting from rest at one end of the runway acquires
its takeoff speed of 600 m/s in 8 s. What is its acceleration?
2)
How far could you travel if you drive at a constant speed of 30
mph for 6 hours?
3)
Driver A is driving in circles at a constant speed of 6 mph.
Driver B started at rest and is now backing out of a parking spot.
Driver C has his gas pedal to the floor but is doing a burnout.
Which of the above drivers are accelerating?
Literal Equations
In Physics we use a lot of equations for a variety of
purposes.
Take a look at the speed equation:
Speed =
distance
time
This equation is solved for speed, but we can find
distance and time using this equation as well. We
just have to rearrange it!
Rearranging Equations
There are 2 rules that you need to remember for
rearranging equations:
1) You can do anything you want as long as you
do it to BOTH sides of the equals sign (=)
2) To move or cancel out part of an equation,
you must do the opposite operation
Opposite Operations
Let’s Practice!
Remember that the words ‘Solve for _____’
simply means you want that variable by itself.
Speed =
distance
time
Solve for distance.
Let’s Practice!
Don’t forget that multiplying only gets rid of
what is on the BOTTOM of a fraction/division.
Speed =
distance
time
Solve for time.
Let’s Practice!
To get rid of a fraction, you multiply by
whatever is on the bottom!
Acceleration =
Vf −Vi
time
Solve for time.
Let’s Practice!
Remember that you must undo any operation
that is happening to a whole chunk of the
equation before you can break that chunk up.
Acceleration =
Vf −Vi
time
Solve for Vi
Let’s Practice!
When you do a division, you can get rid of more
than one multiplication at a time!
Fg =
Gm1m2
r2
Solve for m2
Let’s Practice!
You are able to move large pieces as if they
were one variable if you do not need to break
them up!
d = vi t +
1 2
at
2
Solve for vi
Let’s Practice!
Always move pieces you don’t need to break up
before you do anything else!
d=
vi + vf
2
*t
Solve for vi