Download Acceleration

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
Check Your Understanding
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)
Check Your Understanding
Suppose a car moving in a straight line
steadily increases its speed each
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.
Check Your Understanding
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 = ?
Δvcar=65–50=15 km/h
t = 5s
acar = (15 km/h) / (5s)
atruck = ?
Δvtruck=15-0=15 km/h
t = 5s
atruck = (15 km/h) / (5s)
acar = 3 km/h.s
atruck = 3 km/h.s
Check Your Understanding
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
Velocity – Time Graphs
• Velocity-Time graphs
show the change of
velocity over an
elapsed time
– AKA Speed-Time
graphs
• Remember that speed
does NOT take into
account direction
• Time is always the
independent variable
• Velocity is always the
dependent variable
60
50
40
30
20
10
0
0
10
20
30
40
50
• 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
in the opposite direction
– A zero slope means that the velocity is NOT
changing, meaning that the object is moving at the
same speed in the same direction
Check Your Understanding
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.
Check Your Understanding
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).
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**
Check Your Understanding
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
How about 8 seconds?
v=?
g = 10 m/s2
t = 8s
v = gt
v = (10 m/s2) (8s)
v = 80 m/s
How about 15 seconds?
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)
Check Your Understanding
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.