CALCULATING FORCES OF MOTION

In mathematics you don't
understand things. You just get
used to them.
Johann von Neumann (1903 
1957)

Solving acceleration problems require some of the same
measurements needed for speed and velocity.
The procedure for solving an equation concerning acceleration still
requires the careful stepbystep process used in speed and
velocity problems.
Let's begin. 
EQUATION FOR ACCELERATION:
acceleration = final velocity – initial velocity = D v
time
t
OR a = v_{f} – v_{i} = D v
t t
As always, the best way to learn is to do! Let's work through a problem.
If you need to review solving one step division or subtraction problems,
click below.

Problem #1:
A skater goes from a standstill to
a speed of 6.7 m/s in 12 seconds. What is the
acceleration of the skater?

Step 1:
Write down the equation needed
for solving for acceleration.

a = v_{f} – v_{i} =
D
v
t t

Step 2:
Insert the
known measurements
into the equation.

Known
: The initial speed of the skater was zero
since he was not in motion. The skater finally
reached a speed of 6.7m/s in 12 seconds, which
is the final speed or velocity. The equation will
look like this:
a = 6.7m/s – 0m/s = 6.7m/s =
12s 12s

Step 3:
Solve. Carefully put all
measurements into your calculator.
You must solve the change in velocity
portion of the equation before you can
do the division portion to solve for
acceleration. Don't forget that the SI
unit for acceleration is m/s^{2 .}

SOLUTION:
The skater had an
acceleration of .56m/s^{2 .}
a = 6.7m/s – 0m/s = 6.7m/s = .56m/s^{2}
12s 12s

Now, you give it a try!

PRACTICE PROBLEMS:
1. As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s. Find the average acceleration of the bus. 2. During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25s. What is the sprinter’s average acceleration during this period? 3. A baby sitter pushing a stroller starts from rest and accelerates at a rate of 0.500m/s^{2}. What is the velocity of the stroller after it has traveled for 4.75 minutes? 
INTERNET SITES

LINKS: 
Ready to try some acceleration problems that are a bit more
challanging? Make sure that you have your paper, pencil, and
calculator ready and then click
here.

Not all problems dealing with acceleration are looking for the acceleration
of an object.
Maybe the acceleration of the object is already known and the problem is to find the initial velocity of the object or the time interval that the object was accelerating. In these cases, you will need to isolate the part of the problem for which you are looking. This is known as isolating a variable. If you look below, you will see the acceleration equation as you have been practicing it. You will also see the equation rearranged to find the velocity and the time. 
To find the
acceleration
of an
object:

a= v_{f}  v_{i } =
D
v
t
t

To find the
change in velocity
of an object:

D
v = (a)(t)

To find the
time
it took for an object to accelerate:

t =
D
v
a

These formulas are used by placing the know values given in the problem
into the equation. Always ask yourself, "What is the problem solving for?"
or "What is the problem looking for?", and then choose the correct
formula.
Let's practice a few of these types of problems. 
Solving for speed:


Solving for Time:

