Notes: 11.3
Acceleration
Acceleration
A. The rate at which velocity changes.
* Recall - Velocity is a combination of
speed and direction. The unit for
velocity is meters per second.
B. Acceleration can be described as
changes in speed, direction, or both.
Just like velocity!
Ex.) The acceleration of a carousel.
*The speed of the carousel is not changing
however, you are accelerating. The carousel is
constantly going in circles. This is causing a
continuous change in direction. Which is a
causing a continuous change in acceleration.
Ex.) The acceleration of a roller coaster.
*The roller coaster is constantly speeding up,
slowing down, and changing direction. This is a
constant change in velocity. Not just direction
like the carousel. Since the velocity is
constantly changing, then so is the
acceleration.
Ex.) A plane taking off.
*This is an example of constant acceleration (a
steady change in velocity) . The plane is taking
off in a straight line, but its velocity is changing
by the same amount each second.
Acceleration
C. The unit for acceleration is meters per
second per second or m/s^2.
D. Acceleration can be caused by a positive
change in speed, a negative change in speed
(deceleration), or a change in direction.
Free Fall
E. Free fall is the movement of an object toward
Earth due to gravity.
A. Objects falling near Earth’s surface
accelerate downward at a rate of
9.8m/s^2.
B. This means that every second an object is
in free fall it accelerates at 9.8 meters per
second.
Ex. 1) A rock falling of the top of the top of a cliff.
*How much time passes between
each image of the falling rock?
*How does the distance traveled
change between successive time
intervals?
*How does the average speed change
between successive time intervals?
Ex. 2) A person bouncing a basketball.
*As the ball falls from the person’s hand, how does its speed change?
*What happens to the speed of the ball as the ball rises from the floor to
the person’s hand?
*At what point does the ball have zero velocity?
*How does the velocity of the ball change when it bounces on the floor?
Calculating Acceleration
A. You can calculate acceleration for a straight
line motion by dividing the change in velocity
by the total time.
B. If “a” is acceleration, vi is the initial velocity,
vf is the final velocity, and t is total time then
the equation for acceleration can be written as:
acceleration = change in velocity/ total time
A = (vf - vi) / t
Calculating Acceleration
C. In this equation velocity is in the numerator and
time is in the denominator.
D. If the velocity increases, the numerator is
positive and thus the acceleration is also positive.
Ex. If you are coasting downhill on a bicycle then
your velocity increases and your acceleration is
positive.
Acceleration
E. If the velocity decreases, then the numerator is
negative and the acceleration is also negative.
Ex. If you continue coasting after you reach the
bottom of the hill, your velocity decreases and
your acceleration is negative.
Now lets do some calculations!!! Yeah!!!
Ex.1) Recall the stone falling off of the cliff. Lets
calculate the acceleration for each time interval.
A(1) =
A(2) =
A(3) =
Conclusion:
Ex. 2) A ball rolls down a ramp, starting from rest.
After 2 seconds, its velocity is 6 meters per second.
What is the acceleration of the ball?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Ex. 2) A car traveling at 10 m/s starts to decelerate
steadily. It comes to a complete stop in 20 seconds.
What is its acceleration?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Ex. 3) An airplane travels down a runway for 4.0 seconds with
an acceleration of 9.0 m/s^(2). What is its change in velocity
during this time?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Ex. 4) A child drops a ball from a bridge. The ball strikes the
water under the bridge 2.0 seconds later. What is the velocity of
the ball when it strikes the water?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Ex. 5) A boy throws a rock straight up into the air. It reaches
the highe4st point of its flight after 2.5 seconds. How fast was
the rock going when it left the boys hand?
What do we know?
What do we want to know?
What formula should we use?
Solve!
C. Graphs of accelerated motion
A. You can use a speed time graph to calculate
acceleration. It’s easy!!!
B. The slope of a speed time graph is
acceleration!
C. The slope is the change in speed divided by
the change in time.
D. Find the acceleration
16
12
8
4
0
1
2
3
4
D. Find the acceleration
5
4
3
2
1
0
5
10
15
20