# Speed__Velocity_and_Acceleration

Document Sample

```					Speed, Velocity and Acceleration

Linear Motion
Linear Motion
• The following quantities are used to describe
motion: speed, velocity and acceleration
• Each of these is a rate. A rate is a quantity
divided by time.
• Motion along a straight line is sometimes
called linear motion.
All Motion is relative
• All motion is relative to a reference.
• In our environment, the reference for motion
is the earth’s surface, and speeds are
measured relative to the earth
• The earth moves at 107,000 km/h relative to
the sun
Speed
• Speed is a measure of how fast something is
moving.
• Units of speed could be: km/h, m/s, mi/h, ft/s
• In physics we use units of m/s for speed

•                                 s = d/t
distance
speed                    d

time
s       t
Instantaneous Speed
• Instantaneous speed is speed at any instant in
time.
• A speedometer measures speed in ‘real time’
(the instantaneous speed).
Average Speed
• Average speed is the average of all
instantaneous speeds; found simply by a total
distance/total time ratio
• The average speed of a trip:
total distance
average speed 
elapsed time
Velocity vs. Speed
• Speed refers to how quickly an object moves
• Velocity is defined as speed in a given direction or rate of
change of position (displacement over time). v = x/t
• Velocity refers to both the speed and direction
• Negative velocity means the object is moving in the opposite
direction
• Motion at constant velocity means that both the speed and
direction of an object do not change.
• In a car, we can change the velocity three ways: gas pedal to
speed up, brake to slow down or steering wheel to change
direction
Velocity Triangle
• Speed and velocity triangles are similar
because v = x/t
• Find the equation for displacement, and time
using the triangle
• x=vxt
• t = x/v               x

v    t
Velocity Questions
1) How far does Bob run if he maintains an average
velocity of 3 m/s for 10 s?
2) List three ways you can change the velocity of your
car.
3) Is it possible to go around a corner without
changing velocity? Explain.
4) One car is going 25 miles/hr north, another car is
going 25 miles/hr south. Do they have the same
velocity? Explain.
1.       What is the speed of a truck
that travels 10. km in 10. minutes?
2.       What distance is traveled by
a police car that moves at a constant
speed of 1.5 km/minute for 5.0
minutes?
3.     What distance would be
covered in 10. minutes by a train
that travels at a constant speed of
500. meters every 10. seconds?
4.     What is the average speed
of a commercial jet that travels from
New York to Los Angeles (4800 km)
in 6.00 hours?
6.     A car is traveling at an
average speed of 70. m/s. How
many km would the car travel in 6.5
hours?
The pilot of a light plane heads due
North at an airspeed of 180
km/h. A wind is blowing from
the West at 60. km/h. What is
the plane’s velocity with respect
to the ground?
A car moved 60 meters West in 2
hours. What is its average
velocity?
A moon rock is for the rock to fall 6.6
meters dropped from a cliff and
it takes 2 seconds. What is the
moon rock’s average speed?
A car travels 1000 meters in 5
seconds. What its average velocity?
A boy walks 500 meters in 10
seconds. What is his average
velocity?
Jane rolled a ball 600 meters. What
was her average velocity if it
took her 10 seconds?
What is the average velocity of a dog
that runs 7500 meters that in 10
seconds?
What is the average velocity of a car
that coasts 3000 meters in 300
seconds?
How far will a horse trot at a velocity
of 4 m/s for 1 minute?
What is the average velocity of a
student who walks 800 meters
in 78 seconds?
What is average velocity of a dog
who walks 100 meters in 20
seconds?
An object travels at a velocity of
18.99 m/s for a time period of
15.63 seconds. What is its
displacement?
An object travels at a velocity for a
time period of 12.19 seconds
over a displacement of 10.56
meters. What is the value of this
constant velocity?
An object travels at a constant
velocity of 14.23 m/s for a time
period of 11.19 seconds. What is
its displacement over this time?
An object travels at an average
velocity of 15 m/s for 23
seconds. What is its
displacement over this time?
How long will a dog run at a pace
of 2 m/s over 12 meters?
Acceleration
• For its velocity to change, an object must
accelerate.
• An object accelerates whenever its speed or
direction or both change.
• Acceleration may be positive (increasing speed)
or negative (decreasing speed).
• Acceleration is a measure of how quickly the
velocity changes: a = Dv/t
change of velocity
acceleration 
time interval
Acceleration at constant speed
• An object moving in a circle at constant
speed is always accelerating (changing
direction).
Solving Acceleration Problems using
Acceleration Triangle
• If not, use triangle to find change in velocity (Dv),
then find initial or final velocity
• Dv = ending velocity – starting velocity
• Acceleration = Velocity Final – Velocity Initial
»               Time

Dv

a        t
A dragster going at 15 m/s increases its
velocity to 25 m/s in 4 seconds.
What is its acceleration?
The driver of a car steps on the brakes,
and the velocity drops from 20 m/s to 10
m/s in a time of 2 seconds. Find his
acceleration.
Find the acceleration of a car that travels
at a constant velocity of 45 Km/hr
for 10 s.
Challenge: Calculate the velocity of a
skateboarder who accelerates from
rest for 3 seconds down a ramp at
an acceleration of 5 m/s2.
A roller coaster car rapidly picks up
speed as it rolls down a slope. As it
starts down the slope, its speed is 4
m/s. But 3 seconds later, at the
bottom of the slope, its speed is 22
m/s. What is its average
acceleration?
. A cyclist accelerates from 0 m/s to
8 m/s in 3 seconds. What is his
acceleration ? Is this
acceleration higher than that of a
car which accelerates from 0 to 30
m/s in 8 seconds?
certain car can accelerate from rest
to 70 km/h in 7 seconds. Find the
car’s average acceleration.
4. A lizard accelerates from 2 m/s to
10 m/s in 4 seconds. What is the
lizard’s average acceleration?
5. If a Ferrari, with an initial velocity
of 10 m/s, accelerates at a rate of 50
m/s/s for 3 seconds, what will its
final velocity be?
A skater increases her velocity
from 2.0 m/s to 10.0 m/s in 3.0
seconds. What is the skater’s
acceleration?
A car accelerates at a rate of 3.0
m/s2. If its original speed is 8.0 m/s,
how many seconds will it take the
car to reach a final speed of 25.0
m/s?
While traveling along a highway a
driver slows from 24 m/s to 15 m/s
in 12 seconds. What is the
automobile’s acceleration?
(Remember that a negative value
indicates a slowing down or
deceleration.)
A parachute on a racing dragster
opens and changes the speed of the
car from 85 m/s to 45 m/s in a
period of 4.5 seconds. What is the
acceleration of the dragster?
A car traveling at a speed of 30.0
m/s encounters an emergency and
comes to a complete stop. How
much time will it take for the car to
stop if it decelerates at -4.0 m/s2?
If a car can go from 0 to 60 mi/hr in
8.0 seconds, what would be its final
speed after 5.0 seconds if its starting
speed were 50 mi/hr?
A cart rolling down an incline for 5.0
seconds has an acceleration of 4.0
m/s2. If the cart has a beginning
speed of 2.0 m/s, what is its final
speed?
A helicopter’s speed increases from
25 m/s to 60 m/s in 5 seconds. What
is the acceleration of this
helicopter?
As she climbs a hill, a cyclist slows
down from 25 mi/hr to 6 mi/hr in 10
seconds. What is her deceleration?
A motorcycle traveling at 25 m/s
accelerates at a rate of 7.0 m/s2 for
6.0 seconds. What is the final speed
of the motorcycle?
A car starting from rest accelerates
at a rate of 8.0 m/s/s. What is its
final speed at the end of 4.0
seconds?
After traveling for 6.0 seconds, a
runner reaches a speed of 10 m/s.
What is the runner’s acceleration?
Free fall, an example of
acceleration
• Free fall is when an object is falling being
affected only by gravity. That means NO air
resistance.
Free Fall – All objects fall at the same rate

• If you drop a coin and a feather at the
same time you will notice that the coin
reaches the ground way before the
feather.
• However, if you were to take the air
out of the container you would find
that the coin and feather fall together
and hit the bottom at the same time!
Acceleration due to gravity, g
• Newton told us that every object with mass attracts every
other object with mass and the size of the attraction depends
on the mass of each object and the distance between the
objects
• We don’t feel the attraction of most objects because their
mass is small relative to the Earth which has a huge mass.
• The Earth pulls so that objects experience an acceleration of
about 9.8 m/s2. This acceleration is given a special letter, g.
• g = 9.8 m/s2 This number is important, remember it!
• So during each second an object is in free fall, its velocity
increases by 10 m/s. If the object experiences air resistance its
velocity won’t increase as fast because air resistance will slow
it down.
Challenge Question
• Suppose someone throws a ball
straight upward with a speed of 30
m/s and at the same time throws one
straight down with a speed of 30 m/s.
Which ball will be traveling faster
when it hits the ground, the one
thrown straight upward or the one
thrown straight down? Assume there
is no air resistance.
Time and velocity for an object in free fall
v = gt

v

g       t
Time and Distance for an object in free fall
d = ½ gt2

2d
t
g
Free Fall Questions – How Fast?
1) When a ball is thrown straight down, by how much does speed increase
each second on Earth?
2) When a ball is thrown straight up, by how much does speed decrease each
second?
3) In free fall, do a feather and a ball fall side by side? Explain.
4) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s.
5) Suppose a rock is dropped on a planet where the acceleration due to
gravity it 5 m/s2, by how much would the speed change each second?
6) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the
end of the 3 s interval?
7) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after
6s of free fall.
Free Fall Questions – How Far?
1)   For a freely falling rock does the distance fallen each second stay the
same, increase with time, or decrease with time?
2) A ball is dropped from rest and freely falls for 6 s. How many meters has
it fallen in 6 s?
3) A ball is thrown straight upward and travels 5 m until it reaches the top
of its path.
a) How far will it fall before it reaches its initial position?
b) How long will it take to fall that distance?
c) How long will the ball be in the air?
4) A ball is thrown straight up and returns to Earth 6 s later.
a) Find its speed at the top of its path.
b) Find its acceleration at the top its path.
c) How long does it take to reach the top of its path?
d) How fast is it traveling when it returns to Earth?
e) Challenge: What is its maximum height?
1) If one had only a stopwatch, could one
determine the initial speed of a ball
launched vertically upward from the earth’s
surface? Explain.

2) With only a stopwatch, could one
determine how high the ball travels before
it stops? Explain.
Motion Graphs – Position vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving
rightward but speeding up or accelerating
Motion Graphs – Velocity vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving
rightward but speeding up or accelerating
Motion Graph Questions
1) What do you think might be happening in this graph?

2) What do you think position
and velocity graphs of free
fall motion might look like?
Try to sketch them.

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 42 posted: 8/23/2011 language: English pages: 66