Download Speed, Velocity, and Acceleration

Bellringer
Compare and explain in complete sentences and using
graphs what is velocity and acceleration vs time.
Previous homework
CALCULATE DISTANCE, VELOCITY AT ANY TIME
FOR THE ARROW SHOOT VERTICALLY
IN THE AIR
Current Homework
Calculate distance and velocity for an object with
V0 = 10 m/sec, a = 2 m/sec2, S0 = - 7 m.
1. At any time t
2. At time t = 5 sec, 10 sec, 20 sec.
Formulas:
V (t) = V0 + at, S(t) = S0 + V0 x t + (a x t^2) /2
Force and Motion Standards
Students will investigate the relationship
between force, mass, and the motion of
objects.
• a. Determine the relationship between
velocity and acceleration.
• b. Demonstrate the effect of balanced and
unbalanced forces on an object in terms of
gravity, inertia, and friction.
• Students will investigate the relationship
between force, mass, and the motion of
objects.
• a. Determine the relationship between
velocity and acceleration. Additional
vocabulary: reference point, meter, speed,
average speed, instantaneous speed,
slope, distance, displacement
• b. Demonstrate the effect of balanced and
unbalanced forces on an object in terms of
gravity, inertia, and friction. Additional
vocabulary: newton, net force, mass, weight
Force and Motion Standards
• Students will recognize characteristics of
gravity, electricity, and magnetism as major
kinds of forces acting in nature.
• a. Recognize that every object exerts
gravitational force on every other object and
that the force exerted depends on how
much mass the objects have and how far
apart they are.
What do we need to know and
be able to do?
Essential Question:
• How would you describe how fast an
object is moving?
Supporting Questions:
• How is it possible to be accelerating and
traveling at a constant speed?
• Why is it more important to know a
tornado’s velocity than its speed?
Speed, Velocity, and Acceleration
Goals:
• To investigate what is needed to describe
motion completely.
• To compare and contrast speed and
velocity.
• To learn about acceleration.
To describe motion accurately and completely, a frame of reference is needed.
An object is in motion if it changes
position relative to a reference point.
• Objects that we call stationary—such as a
tree, a sign, or a building—make good
reference points.
The passenger can use a tree as a reference point to decide if the
train is moving. A tree makes a good reference point because it is
stationary from the passenger’s point of view.
Describing Motion
Whether or not
an object is in
motion depends
on the reference
point you choose.
Distance
When an object moves, it goes from point
A to point B – that is the DISTANCE it
traveled. (SI unit is the meter)
Distance is how much ground an object has
covered during its motion.
B
A
Displacement
Knowing how far something moves is not sufficient. You
must also know in what direction the object moved.
Displacement is how
far our of place the
object is; it is the
object’s overall
change in position.
Speed
Calculating Speed: If you know the distance an
object travels in a certain amount of time, you
can calculate the speed of the object.
What is
instantaneous
speed?
Instantaneous
speed is the
velocity of an
object at a
certain time.
Speed = Distance/time
Average speed = Total distance/Total time
Describing Motion
2.1
Velocity
Because velocity depends on direction as well
as speed, the velocity of an object can change
even if the speed of the object remains
constant.
The speed of this car
might be constant,
but its velocity is not
constant because the
direction of motion
is always changing.
Velocity
Velocity is a description of an object’s
speed and direction.
As the sailboat’s direction
changes, its velocity also
changes, even if its speed stays
the same. If the sailboat slows
down at the same time that it
changes direction, how will its
velocity be changed?
Speed v. Velocity
1. How are speed and velocity similar?
They both measure how fast something is moving
2. How are speed and velocity different?
Velocity includes the direction of motion and
speed does not (the car is moving 5mph East)
3. Is velocity more like distance or
displacement? Why?
Displacement, because it includes direction.
Graphing Speed
D
I
S
T
Speed
increasing
Object begins moving at
a different speed
A
N
Object is
stopped
C
E
TIME
The steepness of a line on a graph is called
slope.
• The steeper the slope is, the greater the
speed.
• A constant slope represents motion at
constant speed.
Using the points shown, the rise is
400 meters and the run is 2 minutes.
To find the slope, you divide
400 meters by 2 minutes. The slope is
200 meters per minute.
Formula for Calculating Speed
Speed = Distance time
Problem Solving: Calculating
Speed
What is the speed of a sailboat that is traveling 120 meters in 60 seconds?
Step 1: Decide what the problem is asking? A boat traveled 120 meters in 60
seconds. What was the speed of the boat?
Step 2: What is the formula to calculate speed? Speed = Distance/Time
Step 3: Solve the problem using the formula:
Speed = 120 meters
60 seconds = 2 m/s
So, the boat was traveling at 2 m/s
Now you try:
What is the speed of a car that is traveling 150
miles in 3 hours?
Answer:
Step 1: What are the facts in the problem?
A car is traveling 150 miles in 3 hours.
Step 2: What is the formula to solve the
problem? Speed = Distance/Time
Step 3: Solve the problem.
Speed = 150 miles 3 hours
Speed = 50 miles/hr.
So, the car is traveling 50 miles/hr.
Acceleration
Acceleration is the rate at which velocity
changes.
Acceleration can result from a change in
speed (increase or decrease), a change
in direction (back, forth, up, down left,
right), or changes in both.
• The pitcher throws. The ball speeds toward the
batter. Off the bat it goes. It’s going, going, gone! A
home run!
• Before landing, the ball went through several changes
in motion. It sped up in the pitcher’s hand, and lost
speed as it traveled toward the batter. The ball
stopped when it hit the bat, changed direction, sped
up again, and eventually slowed down. Most examples
of motion involve similar changes. In fact, rarely does
any object’s motion stay the same for very long.
Understanding Acceleration
1. As the ball falls from the girl’s hand, how does its
speed change?
2. What happens to the speed of
the ball as it rises from the ground
back to her hand?
3. At what point does the ball
have zero velocity? When it
stops and has no direction.
4. How does the velocity
of the ball change when
it bounces on the floor?
You can feel acceleration!
If you’re moving at 500mph
east without turbulence,
there is no acceleration.
But if the plane hits an air pocket and drops 500 feet in
2 seconds, there is a large change in acceleration and
you will feel that!
It does not matter whether you speed up or
slow down; it is still considered a change in
acceleration.
In science, acceleration refers to increasing speed,
decreasing speed, or changing direction.
• A car that begins to move from a stopped position or speeds
up to pass another car is accelerating.
• A car decelerates when it stops at a red light. A water skier
decelerates when the boat stops pulling.
• A softball accelerates when it changes direction as it is hit.
Calculating Acceleration
Acceleration = Change in velocity
Total time
So…Acceleration = (Final speed – Initial speed)
Time
Calculating Acceleration
As a roller-coaster car starts down a slope, its
speed is 4 m/s. But 3 seconds later, at the
bottom, its speed is 22 m/s. What is its
average acceleration?
What information have you
been given?
Initial speed = 4 m/s
Final Speed = 22 m/s
Time = 3 s
Calculating Acceleration
What quantity are you trying to calculate?
The average acceleration of the roller-coaster car.
What formula contains the given quantities and the
unknown quantity?
Acceleration = (Final speed – Initial speed)/Time
Perform the calculation.
Acceleration = (22 m/s – 4 m/s)/3 s = 18 m/s/3 s
Acceleration = 6 m/s2
The roller-coaster car’s average acceleration is 6 m/s2.
Graphing acceleration
S
P
E
Object
accelerates
Object decelerates
E
D
Object moves
at constant
speed
Time
Now You Try:
A roller coasters velocity at the top
of the hill is 10 m/s. Two seconds
later it reaches the bottom of the hill
with a velocity of 26 m/s. What is
the acceleration of the coaster?
The slanted, straight line on this speed-versus-time graph tells you that
the cyclist is accelerating at a constant rate. The slope of a speedversus-time graph tells you the object’s acceleration. Predicting How
would the slope of the graph change if the cyclist were accelerating at a
greater rate? At a lesser rate?
Since the slope is increasing, you can conclude that the
speed is also increasing. You are accelerating.
Distance-VersusTime Graph The
curved line on this
distance-versus-time
graph tells you that
the cyclist is
accelerating.
Acceleration Problems
A roller coaster is moving at 25 m/s at the
bottom of a hill. Three seconds later it reaches
the top of the hill moving at 10 m/s. What was
the acceleration of the coaster?
Initial Speed = 25 m/s
Final Speed = 10 m/s
Time = 3 seconds
Remember (final speed – initial speed) ÷ time is acceleration.
(10 m/s – 25 m/s) ÷ 3 s = -15 m/s ÷ 3 s = -5 m/s2
This roller coaster is decelerating.
A car’s velocity changes from 0 m/s to 30
m/s in 10 seconds. Calculate acceleration.
Final speed = 30 m/s
Initial speed = 0 m/s
Time = 10 s
Remember (final speed – initial speed) ÷ time is acceleration.
(30 m/s – 0 m/s) ÷ 10 s = 30 m/s ÷ 10 s = 3 m/s2
A satellite’s original velocity is 10,000 m/s.
After 60 seconds it s going 5,000 m/s. What
is the acceleration?
Remember (final speed – initial speed) ÷ time is acceleration.
Final speed (velocity) = 5000 m/s
Initial speed (velocity) = 10,000 m/s
Time = 60 seconds
(5000 m/s – 10,000 m/s) ÷ 60 s = -5000 m/s ÷ 60 s
= -83.33 m/s2
**This satellite is decelerating.
• If a speeding train hits the brakes and it
takes the train 39 seconds to go from 54.8
m/s to 12 m/s what is the acceleration?
Remember (final speed – initial speed) ÷ time is acceleration.
Final speed= 12 m/s
Initial speed= 54.8 m/s
Time = 39 s
12 m/s – 54.8 m/s ÷ 39 s = -42.8 m/s ÷ 39 s
= -1.097 m/s2
This train is decelerating.