11.3 Acceleration
Acceleration is the rate at which velocity changes.
It can be described as changes in speed, changes in direction, or changes in both.
IT IS A VECTOR - so it has direction
These changes can be increases or decreases.
Negative acceleration is called deceleration.
Because acceleration is the rate of change in velocity, and the units for velocity are m/s.
The units for acceleration are meters per second squared (m/s2).
Free Fall is acceleration due to gravity. G = 9.8 m/s
2
Free fall is an example of acceleration due to a change in speed.
A drag race at Norwalk Raceway Park is also an example of acceleration due to a change in
speed. (The drag strip is a straight path – the cars do not turn.)
Acceleration can also occur without a change in speed – just with a change in direction.
Riding on a carousel (merry-go-round) is an acceleration due to just a change in direction.
A roller coaster is an example of acceleration due to changes in both speed and direction.
Constant acceleration is a steady change in velocity. (The velocity of the object changes by
the same amount each second.)
A jet taking off could be an example of constant acceleration.
Graphs of Acceleration
Acceleration is generally graphed one of two ways:
distance-time graphs, and speed-time graphs.
Distance-time graphs
Graphs are non-linear. (They are curved.)
An increasing slope means speed is increasing (the object is accelerating). (See figure 1)
Speed-time graphs
For this class, the graphs are linear.
Constant acceleration is a straight line.
The slope of the line is acceleration: (see figures 2 and 3)
Positive slope (line going up) means acceleration.
Negative slope (line going down) means deceleration.
Zero slope (horizontal line) means zero acceleration (constant velocity).
Instantaneous Acceleration is how fast velocity is changing in a given instant.
Calculating Acceleration
You calculate acceleration for straight-line motion by dividing the change in velocity by the
total time.
Change in velocity
(vf - vi )
Acceleration = ————————— = ————————
Total time
t
vf is the final velocity, and vi is the initial velocity
Notice that if the final velocity is greater than the initial velocity, the object’s acceleration is
positive (the object’s speed increased). If the final velocity is less than the initial velocity,
the object’s acceleration is negative (deceleration) (the object’s velocity decreased).
If a problem involves throwing an object into the air, or dropping an object, the acceleration
is gravity (G = 9.8 m/s2) down toward earth. The object will decelerate as it travels up
against gravity, and will accelerate as it travels down with gravity.
Formulas
1.) Read and understand what information you are given, and what you are trying to find.
2.) Choose the correct formula to calculate.
3.) Be sure all of you units agree.
4.) Replace each variable in the formula with the given quantities, and do the math.
5.) Give your answer with the correct units.
6.) Look at your answer to be sure it is reasonable, and it is the unknown you were trying
to find.