1. Acceleration a

2. Acceleration What do you think of when someone says acceleration?
If you think speeding up – then you are almost completely correct!!!!
It turns out that an object is accelerating if it
Speeds up
Slows down
Or changes direction

3. Defining Acceleration
Acceleration is defined as the rate of change of velocity.
Another way to say this is that acceleration measures how fast an objects velocity changes.
Accelerations can be positive or negative
But
Positive acceleration doesn’t always mean an object is speeding up.
Negative acceleration doesn’t always mean an object is slowing down.

4. Speeding Up or Slowing Down
For linear motion (straight-line). Whether or not an object speeds up or slows down is determined by the direction of the acceleration COMPARED to the direction of motion (velocity).
If an object is moving in the negative direction and its acceleration is also positive, then the object will slow down.
If an object is moving in the positive direction and its acceleration is also positive, then the object will speed up.
If an object is moving in the negative direction and its acceleration is also negative, then the object will speed up.
If an object is moving in the positive direction and its acceleration is also negative, then the object will slow down.
In general, if the acceleration and velocity have the same sign (both positive or both negative), then the object: v v v v
SPEEDS UP a a a a
In general, if the acceleration and velocity have different signs (one positive and one negative), then the object:
SLOWS DOWN

5. Units for Acceleration
English System
Feet per Second per Second (ft/s/s or ft/s2)
Metric System
Kilometers per Hour per second (km/hr/s), Meters per Second per Second (m/s/s or m/s2))
In science the most common unit is:
m/s/s or m/s2

6. Meaning of Acceleration
A car starts from rest and accelerates at 4 km/hr/s. What does this mean?
This means the car’s velocity changes by 4 km/hr each second.
Starting Velocity:
Velocity after 1-s:
Velocity after 2-s:
Velocity after 10-s:
0 km/hr
4 km/hr
8 km/hr
40 km/hr

7. Meaning of Acceleration
A car traveling at 10 km/hr accelerates at 4 km/hr/s. What does this mean?
This means the car’s velocity changes by 4 km/hr each second.
Starting Velocity:
Velocity after 1-s:
Velocity after 2-s:
Velocity after 10-s:
10 km/hr
14 km/hr
18 km/hr
50 km/hr

8. Meaning of Acceleration
A car traveling at 8 km/hr accelerates at-4 km/hr/s. What does this mean?
This means the car’s velocity changes by -4 km/hr each second.
Starting Velocity:
Velocity after 1-s:
Velocity after 2-s:
Velocity after 10-s:
8 km/hr
4 km/hr
STOPPED!!!!!!
0 km/hr
CHANGED DIRECTIONS
-32 km/hr

9. Solving Problems with Acceleration
Acceleration is defined as the rate of change of velocity. Since this is a rate of change we can also say that acceleration is the change in velocity over time. As an equation this looks like:
vf is the final velocity (ending) and vi is the initial velocity (starting).
This will find the average acceleration if the change in velocity is over a time interval.
This will find the uniform acceleration if the acceleration is constant.

10. Solving Problems with Acceleration
If we place this formula into our triangle, we can find other useful formulas from this
vf - vi a t

11. Solving Problems with Acceleration
If you need to find t, cover t.
Since vf - vi is on top of a, divide them.
vf - vi a t

12. Solving Problems with Acceleration
If you need to find vf, cover vf-vi.
Since a is next to t, multiply them.
Finally add vi to both sides.
vf - vi a t