Uniformly Accelerated Motion
Galileo Galilei (15641642)
Hypothesis: At a given
location on the Earth and
in the absence of air
resistance, all objects fall
with the same constant
•Free Fall—the motion of a body when
only the force due to gravity is acting on
the body.
•The force due to gravity is constant.
•Because the force of gravity is constant,
the acceleration due to gravity is also
•Acceleration due to gravity on Earth is
denoted with the symbol g and has a
magnitude of 9.80 m/s2.
•In British units, g = 32 ft/s2.
•Air resistance is often considered
negligible when we are analyzing freelyfalling bodies.
•However, if the velocity becomes very
large, air resistance can also become
•A constant maximum velocity can be
reached when an object is falling in air
called terminal velocity.
•This occurs as the air resistance
increases enough to equal the force to
•Remember: the acceleration due to
gravity is a vector quantity. Therefore, it
has magnitude and direction.
•Its magnitude is 9.80 m/s2 with a
direction downward toward the center of
•It is extremely important to pay attention
to your frame of reference (what
direction motion is), here. Assign +/- to
your acceleration!
•Most of the time, g will be negative
because it is a downward acceleration.
•Since g is a constant acceleration, we
can use our kinematic equations to
solve for a missing quantity…
•Substitute g for a
•For vertical motion, use y in place of x.
1 D Kinematics Alphabet Soup...what do these
letters mean!
a = acceleration
d = distance or displacement
g = acceleration due to gravity
s = speed
t = time
v = velocity
xi = initial position
xf = final position
Basic Kinematic
with muscle!
d = x f - xi
s = d/t
vf = vi + at
v = d/t
xf = xi + vit + ½ at2
a = (vf - vi)/t
vf2 = vi2 + 2a(xf – xi)
vavg = 1/2 (vf + vi)
•It is arbitrary whether we choose y to be
positive in the upward direction or in the
downward direction; but we must be
consistent about it throughout a
problem’s solution.
•Practice, Practice, Practice!!!
One of the fastest airplanes is the
Lockheed SR-71. If an SR-71 flies 15.0 km
west in 15.3 s, what is its average velocity
in km per hour?
Where do we start???
1. Write the given information.
2. Decide what to solve for.
3. Check units for any conversions.
4. Substitute values and do the math.
5. Check work and units.
A walrus accelerates from 7.0 km/h to 34.5
km/h over a distance of 95 m. What is the
magnitude of the walrus’s acceleration?
A bicyclist accelerates--0.870 m/s2 during
a 3.80 s interval. What is the change in
velocity of the bicyclist and bicycle?