1. Acceleration
Average acceleration is the change in velocity divided by time
…the rate of change of velocity…
aavg = ∆v/∆t = (vf – vi)/(tf – ti) [units = m/sec2 or m/sec/sec]
Acceleration is the slope of a line on a time-velocity graph
Positive acceleration means the velocity becomes more positive
Negative acceleration means the velocity becomes more negative

2. Speeding Up or Slowing Down?
Velocity
Acceleration
Description of Motion +
Speeding up in positive direction –
Speeding up in negative direction
Slowing down in the positive direction
Slowing down in the negative direction
+ or –
zero
Maintaining constant velocity
Speeding up from rest
Remaining at rest

3. Fundamental Types of Linear Motion
Uniform motion = motion at a constant velocity (no acceleration)
Initial position, final position, displacement, velocity, and time can be found using velocity equation
vavg = ∆x/∆t = (xf – xi)/∆t

4. Fundamental Types of Linear Motion
Uniform accelerated motion = motion with constant acceleration
Displacement, velocity, and time can still be found using velocity equation
vavg = ½ (vi + vf) = ∆x/∆t
Initial velocity, final velocity, acceleration, and time can be found using the acceleration equation
aavg = ∆v/∆t = (vf – vi)/∆t

5. The Commonly Used Equations
Displacement after a period of uniform acceleration
∆x = vi ∆t + ½ a (∆t)2
xf – xi = vi ∆t + ½ a (∆t)2
xf = xi + vi ∆t + ½ a (∆t)2

6. The Commonly Used Equations
Final velocity after any displacement
vf2 = vi2 + 2 a ∆x

7. Falling Objects
Falling objects are subject to constant acceleration due to gravity
The acceleration of gravity: g = m/sec2
Objects “falling upward” are still subject to the acceleration of gravity
“Free fall” occurs in the absence of air resistance (or when it is ignored)
The equations for falling objects are the same as those for uniform accelerated motion (with g substituted for a)