Acceleration
Instantaneous Velocity =
Acceleration * Time
vinstant= a • t
Let’s look at a sample problem.
Acceleration
You and your friends build a robot built for
running. You run some trials and find that the
robot can go from 1.5 m/s to 6 m/s over the
span of 2.25 seconds.
What is the average acceleration of your
robot?
Acceleration (cont.)
In your next test, you allow the robot to
accelerate at a constant rate of 2 m/s2.
What is the robot’s instantaneous speed at:
0.5 seconds?
1 second?
2 seconds?
3.5 seconds?
4.5 seconds? 5.5 seconds?
Acceleration
How long of a piece of road would you
need in order to conduct all of these
tests?
There’s another equation we need to
learn about:
Displacement = ½ • acceleration • time2
d = ½ • a • t2
Acceleration (cont.)
How long of a piece of road would you need in
order to conduct all of these tests?
Displacement traveled at:
0.5 seconds?
1 second?
2 seconds?
3.5 seconds?
4.5 seconds? 5.5 seconds?
New Displacement Formula
What was our old formula for displacement?
Displacement = Velocityinitial • Time
d = vi • t
If we combine our old and new displacement
formulas, we get:
d = di + vi • t + ½ • a •
2
t
Another Acceleration
When do you feel acceleration during your
life?
What about when you drive?
Do you ever feel this motion when you go
around turns?
How is that acceleration?
Is your velocity changing?
Another Acceleration
How did we define acceleration?
Acceleration is the rate at which velocity of an
object changes.
How is velocity different than speed?
Velocity has direction and speed.
What is changing as you go around a turn?
Another Acceleration
Your direction is changing!
This type of acceleration is
called centripetal acceleration
It also has a formula:
Centripetal Acceleration =
ac = v2 / r
୴ୣ୪୭ୡ୧୲୷ଶ
୰ୟୢ୧୳ୱ ୭୤ ୲୦ୣ ୡ୳୰୴ୣ
Sample Problem (cont.)
After your robot has accelerated to a speed of
11 m/s, it rounds a corner of radius of 5.5 m.
What is the centripetal acceleration
experienced by your robot?
Sample Problem (cont.)
Your robot is running out of gas, and while
traveling at a speed of 11 m/s, it starts to
decelerate at a rate of 2.5 m/s2.
It eventually comes to a stop 8.8 seconds
later. What distance does your robot travel
while coming to a stop?
Kinematics
We now have more equations than we know
what to do with.
Here’s every single kinematic equation we will
be using:
d = d୧ + v୧ • t + ½ • a • t2
v୤ = v୧ + a • t
d=
୴౟ ା ୴౜
ଶ
v୤ଶ = v୧ଶ + 2 • a • d
•t
aୡ =
୴ଶ
୰
Let’s go through the process of figuring out
when to use which equation.
Selecting the Right Tool for
the Job
A car begins at rest at a stoplight. After the
light turns green, the car begins to accelerate
5 m/s2 over the span of 3.6 seconds. What is
the car’s displacement over this period of
time?
What pieces of information are we given?
What equation should we use?
Selecting the Right Tool for
the Job
A rock tied to a string is traveling at a constant
speed of 3 m/s in a circle of radius 2 m.
Calculate the magnitude of the centripetal
acceleration of the rock.
What pieces of information are we given?
What equation should we use?
Selecting the Right Tool for
the Job
A penny is dropped from the top of the Empire
State Building. If the acceleration due to
gravity is -9.8 m/s2, and the Empire State
Building is 381 meters tall, how long does it
take for the penny to hit the ground?
What pieces of information are we given?
What equation should we use?
Selecting the Right Tool for
the Job
A car traveling at 27 m/s slams on its brakes
to come to a stop. It decelerates at a rate of
8 m/s2. What is the stopping distance of the
car?
What pieces of information are we given?
What equation should we use?
Selecting the Right Tool for
the Job
A person walking with a stroller at a rate of
1.5 m/s accelerates at a rate of 0.275 m/s2.
What is the velocity of the stroller after it has
traveled 6.45 m?
What pieces of information are we given?
What equation should we use?