Transcript Velocity and Acceleration

Right now you are traveling approximately:
A) 0 mph
Relative to guy next to you
B) 900 mph Relative to earth’s axis of rotation
C) 67,000 mph Relative to the sun’s center
D) 1.8 times the speed of light (335,000 mi/s)
Relative to the point on the opposite side of the
expanding universe according to Hubble and
Einstein
E) All of the Above
All Motion is Relative!
When is anything ever completely still?
How do you describe the motion of a
turning wheel or a falling piece of paper?
How fast are you traveling if you are sitting
in a supersonic airplane?
 Unless otherwise specified, all motion is
relative to the surface of the earth!
Distance v. Displacement
• Simply put, distance is the magnitude (size)
of displacement.
• 5.0 m away is an infinite number of
locations (because of infinite directions)
• 5.0 m, North is a single value!
• Distance is a scalar quantity!
• Displacement is a vector quantity!
Vector v. Scalar Quantities
Vector Quantity
Fully described by both
magnitude (number
plus units) AND
direction
Represented by arrows
-velocity
-acceleration
-force
Scalar Quantity
Fully described by
magnitude (number
plus units) alone
-mass
-temperature
Vector values are represented by arrows!
Adding vectors that lie along a straight line:
3 m, North
+ 4 m, North = 7 m, North
3 m, North + 4 m, South = 1 m, South
Resultant vectors
Head to tail method 
Vector diagrams are not used when adding
vectors in one dimension (along a line):
3 m, North
+ 4 m, North = 7 m, North
3m+4m=7m
or
-3 m + -4 m = -7 m
3 m, North + 4 m, South = 1 m, South
3 m + (-4 m) = -1 m or
-3 m + 4 m = 1 m
For a vector-- Sign does not represent
value, it represents direction!
Traditionally: Up/Right (+) Down/Left (-)
Vectors exist in one, two and three dimensions!
For now, we will only deal with vectors in one
dimension….
…therefore the direction of the vectors will be
represented by + and - signs
Following the conventions of
the coordinate axis system:
Up/Right (+)
Down/Left (-)
Speed and Velocity
in one dimension
Speed is the magnitude of velocity- it only
reflects how fast an object is traveling
Velocity is a vector- it is speed in a
particular direction
Along a straight line direction is
indicated with a +/- sign
Again: Up/Right is positive and…
Down/Left is negative
Speed v. Velocity
A old man leaves his house, walks 1mile North in
1 hour, turns and walks 1 mile east in 1 hour, turns
and walks 1 mile south in 1 hour, and then turns
and walks 1 mile west in 1 hour. What was his
average speed? What was his average velocity?
Average speed is total distance divided by
total time: v = ∆d/∆t = 4 mi / 4 hr = 1 mi/h
Average velocity is total displacement divided by
total time:
v = ∆d/∆t
0 mi/h
Calculating Velocity
• Average velocity is the total displacement
divided by the total time:
vav = ∆d = d – d0
∆t
t – t0
∆(delta) means “change in”
t final (the last during that time period)
t0 initial (the first during that time period)
•Instantaneous velocity is the velocity of the object at any
given instantGBS Physics.
•Constant (uniform) velocity means non-changing (non-zero)
velocity.
Equation Notations in Physics:
Quantities are expressed in variable form with a
subscript used to describe different points in
time
v = d – d0
or d2 - d1
t – t0
t2 - t1
The bar over the variable means the average
quantity– in this case speed/velocity
Speed/Velocity are derived quantities and have
derived units of length/time
Standard unit:
m/s
sometimes
km/h
1) You drive 18.0 km to school in 30.0 minutes.
Because of bad weather, it takes you 45.0 minutes
to get home from school. What was your average
velocity (km/h)? What was your average speed?
2) Two trains travel toward each other on parallel
tracks at the same speed. At one point, they are
9.0 km apart and they meet 6.0 minutes later.
What is the velocity of each train?
3) A remote control car zips 60.0 m in 6.0 s away
from the remote driver, abruptly reverses and stops
4.8 s after reversing at a point 18 m in front of the
driver. What was the average speed of the car?
What was it’s average velocity?
t0
t1
t (s)
0
1
2
3
4
v (m/s)
0
1
2
3
4
t2
t3
d (m)
0
.5
1.5
2.5
3.5
∆v (m/s)
1
1
1
1
Speed gain: 1 m/s
per every second
t4
The Nature of Acceleration
Acceleration is the change in velocity
divided by the change in time- the rate at
which the velocity changes-GBS Phys
If an object speed up, it accelerates!
If an object slows down, it accelerates!
If an object does not change speed, but
changes direction, it accelerates!
-this is the case when an object travels in
a circular path at constant speed
Calculating Acceleration
We are only going to be concerned with
acceleration in a straight line-- FOR NOW!
Acceleration is a vector, so in a straight line the
direction will be represented by +/- sign.
Negative acceleration means opposite direction!
Average acceleration is change in velocity
divided by change in time.
Uniform acceleration mean constant, non-zero
acceleration!
aav = v - vo
∆t
This is the basic definition of
acceleration in the form of an
equation.
m/s2unit of acceleration (meter per second per
second)
The following equations are basic equations which
are derivations of our basic definitions of velocity
and acceleration:
v = vo + a∆t
∆d = vo∆t +
1
2
a∆t2
v = √vo2 + 2a∆d
A car accelerates from rest at a rate of 2.00 m/s2
for 8.50 s. How fast is the car moving now?
How far did it move during this time?
vo = 0
v = vo + a∆t
a = 2.00 m/s2
= 0 + (2.00 m/s2)(8.50 s)
∆t = 8.50 s
= 17.0 m/s
v=?
∆d = ?
∆d = vo∆t + .5a∆t2
= .5(2.00 m/s2)(8.50s)2
= 72.3 m
1) An object is accelerated to 35.0 m/s at a rate of 2.00
m/s2 for a time of 7.34 s. How far did it move during
this time? [203 m]
2) How far does an object travel if it accelerates from
12.0 m/s to 45.0 m/s in 15.3 s? [436 m]
3) An object traveling 48.7 m/s is brought to a stop
in 7.61 s. How far did the object move during this
time? [185m]
4) An object rolled up a hill will stop after
having traveled up the hill 18.0 m. If the object
is slowed at a rate of 2.50 m/s2, how long will it
take to stop rolling? [3.80s]
1) A ball starting from rest rolls down an incline
and accelerates at the rate of 1.50 m/s2. The total
length of the incline is 80.0 m. Will the ball reach
the bottom after 10.0 s?
2) A car traveling at 35.0 m/s slows down at the rate
of 1.50 m/s2 for 7.00 s. How far does the car travel
in this time?
3) A bicyclist slows his bike from 25.0 m/s to 5.00
m/s over a distance of 75.0 m How long must this
have taken?
Freefall
An object whose motion is only affected by
the acceleration rate due to gravity.
To keep it simple, we will ignore all the
affects of air resistance on all objects in
freefall.
With no air resistance, a potato chip will
fall at the same rate as a bowling ball.
All objects in freefall will have the same
acceleration-- the acceleration due to
gravity: g = 9.80 m/s2
Freefall or Not Freefall?
An airplane in flight?
Not Freefall-air and motors involved!
A floating balloon?
Not Freefall-floats on air
A dropped rock?
Freefall
A ball thrown straight up?
Freefall-up or down is irrelevant!
Solving Freefall Problems
• The acceleration is an accepted value of
9.80 m/s2 (does not count for SD!)
• This acceleration will probably NOT be
explicitly stated in the problem.
• Traditionally, in Physics, up is positive and
down is negative.
• Therefore, for us, acceleration due to
gravity will be a negative value whether the
object is rising or falling!
A ball is launched vertically upward with a
velocity of 115 m/s. A) To what height will it
rise?B)How long will it take the ball to fall
back to the earth?
2 - v2
v
i
A) ∆d = f
vo = 115m/s
2a
2
a= g = - 9.80m/s
= 0 - (115m/s)2
v=0
2)
2(9.80
m/s
A) ∆d = ?
B) ∆ttotal= ?
= 675 m (Positive
meaning in the up
direction!)
B) ∆t = v - vo
v = - 115 m/s
a
= -115 m/s - (115 m/s)
- 9.80 m/s2
Another method:
B) ∆t =
v - vo
a
= 23.4 s
v=0
= 11.7 s X 2 = 23.4 s
1) A baseball is thrown down from the roof of a
building and it hits the ground 1.17 s later with a
speed of 41.5 m/s. How far is the roof above the
ground?
2) A batter pops a ball straight up with a speed of
30.0 m/s. How long does the catcher have to catch
it, assuming he catches it at the same level as the
bat? How high will the ball rise?
3) A student wants to throw a ball upward so that it
reaches an exact height of 20.0 m above the point
where he lets the ball go. With what speed must he
throw the ball? How long will the ball be in the
air?
4) A man holds a ball of mass 1.5 kg out over a
sheer cliff that is 75.0 m above the ground. The
man throws the ball straight up with a speed of
25.0 m/s, but he fails to catch the ball as it falls
back. With what velocity will the ball hit the
ground? How long will the ball be in the air?
5) A hot air balloon is ascending with a speed of
4.00 m/s and is 102 m above the ground when it
releases a sandbag. How much time do the people
below the balloon have to get out of the way of that
sandbag?
End Notes
GBS Acceleration Demo
Which car(s) travel at constant speed?
Which car(s) travel with acceleration?
Which car(s) have the greatest acceleration?
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