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

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

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

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

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

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

Falling Objects Falling objects are subject to constant acceleration due to gravity The acceleration of gravity: g = -9.81 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)