# Projectile Motion Projectile motion is motion that

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```					Accelerated Motion
Changing motion
• You can feel the difference between
uniform and nonuniform motion
• When motion changes, you feel a push or
pull (a force).
– Ex: a Marta train coming to a sudden stop
• In uniform motion, your body becomes
used to it.
– Ex: sitting in a car on cruise control
Acceleration
• Whenever we change our state of motion,
we are accelerating.
• Acceleration is how quickly we are
changing our velocity
• Acceleration: the rate at which
velocity is changing
– SI unit: m/s2 or meters per second per
second
– Ex: speeding up, slowing down (negative
acceleration), changing direction
If a dog chases its tail in a circle at the
same speed the whole time, is it
accelerating?
Yes! Even though its speed is staying
constant, it is changing direction, and
therefore changing its velocity. If the
velocity changes, it is accelerating.
– Equation:   a = Δv / t = (vf – vi) / t
• a = acceleration (m/s2)
• Δv = change in velocity (m/s)
• vf = final velocity (m/s)
• vi = initial velocity (m/s)
• t = time (s)
Suppose a car moving in a straight line
second, first from 35 to 40 km/h, then
from 40 to 45 km/h, then from 45 to 50
km/h. What is its acceleration?

 We see that the speed increases by 5
km/h each second. The acceleration
would be 5 km/h.s during each interval.
In 5 seconds a car moving in a straight line
increases its speed from 50 km/h to 65
km/h, while a truck goes from rest to 15
km/h in a straight line. What is the
acceleration of each vehicle?
a = Δv / t
acar = ?                  atruck = ?
Δvcar=65–50=15 km/h       Δvtruck=15-0=15 km/h
t = 5s                             t = 5s
acar = (15 km/h) / (5s)   atruck = (15 km/h) / (5s)
acar = 3 km/h.s           atruck = 3 km/h.s
Which undergoes a greater acceleration?

Although the speeds are different, their
rate of change of speed is the same…so
both have the same acceleration.
Elapsed Time
Elapsed time: the time that has passed
since the beginning of a fall
– How long it takes something to fall
– SI unit: seconds
Free Fall
• Consider an apple falling from a tree. We
know that it starts at rest and gains speed
as it falls, or accelerates.
• Gravity causes the apple to accelerate
downward and is said to be in free fall.
Free fall: when an object is only
affected by gravity
– SI unit: m/s2 ( for acceleration due to gravity)
– Ex: g = 10 m/s2 on Earth.
• The letter g represents the acceleration due to
gravity.
– Equation:   v = gt
• v = velocity or speed (m/s)
• g = acceleration due to gravity (10 m/s2 on
Earth)
• t = elapsed time (s)

**Hint - as soon as you see any of the
following phrases in a word problem, write
g = 10 m/s2 for a given: free fall, falling,
dropped, thrown**
What would the speedometer reading on
a falling rock be 4.5 seconds after it
drops from rest?

v = ?
g = 10 m/s2
t = 4.5s
v = gt
v = (10 m/s2) (4.5s)
v = 45 m/s
v=?
g = 10 m/s2
t = 8s
v = gt
v = (10 m/s2) (8s)
v = 80 m/s

v=?
g = 10 m/s2
t = 15s
v = gt
v = (10 m/s2) (15s)
v = 150 m/s
• Now consider an object thrown straight up.
It will continue to move straight up, then it
comes back down.
• At the highest point, the object changes its
direction and the objects instantaneous
speed is 0 m/s.
• Whether the object is moving up or down,
the acceleration of the object is always 10
m/s2.
• Because an object in free fall increases
the rate of distance covered every second,
we cannot use v =d/t.
– Equation: d = ½ gt2
• d = distance (m)
• g = acceleration due to gravity (10 m/s2 on
Earth)
• t = elapsed time (s)
What is the distance an object falls in one
second?
d = ?
g = 10 m/s2
t=1s
d = ½ gt2
d = ½ (10)(12)
d=5m
Air Resistance and Free Fall
• All objects fall at 10 m/s2 on Earth
• Regardless of weight or mass
• Ex: In a vacuum, a feather and a bowling ball will hit
the ground at the same time if dropped from the same
hieght
• A vacuum is anyway without any air (ex: outer space)
• Air resistance causes objects such as a coin and
a feather to accelerate differently.
• However, air resistance less noticeably affects the
motion of more massive objects like stones and
baseballs.
• With negligible air resistance, falling objects can
be considered to be in free fall.
Velocity – Time Graphs
• Velocity-Time graphs
60
show the change of
velocity over an           50

elapsed time               40
– AKA Speed-Time
30
graphs
• Remember that speed   20
does NOT take into
account direction     10

• Time is always the         0
0   10   20   30   40   50
independent variable
• Velocity is always the
dependent variable
• The slope of a Velocity-Time graph is equal to
acceleration
• Slope = rise/run
• Slope = change in velocity / time
– a = Δv / t
– The steeper the slope, the faster the acceleration
• Remember acceleration can be speeding up, slowing down,
or sharp turns
– A positive slope is speeding up and moving forward
– A negative slope is EITHER slowing down OR moving
backwards
– A zero slope means that the velocity is NOT
changing, meaning that the object is moving at the
same speed in the same direction
Which person(s) could
be slowing down?
 Person C. They have
a negative slope; they
could be moving
backwards too (there
is not enough info on
the graph to tell).
Which person(s) are
not accelerating?
 A and E. Their have
a constant velocity.

Which person(s) could
be speeding up?
 B and D. They are
increasing velocity
each second.

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