Average Acceleration
„
„
Changing velocity (non-uniform)
means an acceleration is present
Acceleration is the rate of change
of the velocity
a=
„
∆v v f − v i
=
∆t
tf − ti
„
Instantaneous Acceleration
a = lim
a=
∆v
∆t → 0 ∆ t
„
Units are m/s² (SI), cm/s² (cgs),
and ft/s² (US Cust)
Uniform or constant
Acceleration
„
Instantaneous Acceleration
=
vf − vi
tf − ti
The slope of the line tangent to
the velocity-vs.-time graph is
defined to be the instantaneous
acceleration at that time
Acceleration
Velocity vs. time curve is a straight line
„
Most of the problems we will
do will have constant a.
„
„
Vector quantity
When the sign of the velocity and
the acceleration are the same
(either positive or negative), then
the speed is increasing
When the sign of the velocity and
the acceleration are in the opposite
directions, the speed is decreasing
Very important statement
Kinematic Equations
„
Used in situations with uniform
acceleration to find out unknown
quantities using given values.
Kinematic Equations
v = vo + at
∆x = v o t +
1 2
at
2
v 2 = vo2 + 2a∆x
(1)
(2)
(3)
 v + vf 
∆x = v average t =  o
t
 2 
1
Notes on the equations
Notes on the equations
 v + vf 
∆x = v average t =  o
t
 2 
v = vo + at
„
„
Shows velocity as a function of
acceleration and time
Use when you don’t know and
aren’t asked to find the
displacement
Notes on the equations
∆x = v o t +
„
„
„
„
„
Gives displacement as a function
of velocity and time
Use when you don’t know and
aren’t asked for the acceleration
Notes on the equations
1 2
at
2
Gives displacement as a function
of time, velocity and acceleration
Use when you don’t know and
aren’t asked to find the final
velocity
Free Fall
„
„
All objects moving under the influence
of gravity only are said to be in free fall
All objects falling near the earth’s
surface fall with a constant acceleration
The acceleration is called the
acceleration due to gravity, and
indicated by g
v 2 = vo2 + 2a∆x
„
„
Gives velocity as a function of
acceleration and displacement
Use when you don’t know and
aren’t asked for the time
Acceleration due to
Gravity
„
Symbolized by g
g = 9.80 m/s²
„
g is always directed downward
„
„
„
„
When estimating, use g ≈ 10 m/s2
toward the center of the earth
Ignoring air resistance and assuming g
doesn’t vary with altitude over short
vertical distances, free fall is constantly
accelerated motion
2