Upload
oberon
View
43
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Speed, velocity and acceleration. Motion. When an object changes its position, motion has occurred. Distance- How far an object has moved . Displacement- How far an object has moved in relation to its starting point . Consider direction - PowerPoint PPT Presentation
Citation preview
Speed, velocity and acceleration
Motion
• When an object changes its position, motion has occurred.– Distance- How far an object has moved.– Displacement- How far an object has moved in
relation to its starting point.– Consider direction
Example: Two runners travel along the same straight path in a straight line for 500 meters. At the end of the run their distances are the same but their displacements are different. How can this be so?
1 Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.
Comment on their their argument.
Me, as I spent less time on the
trip.
No, I travelled longer distance every
minute.
Who runs faster?
SPEED Distance an object travels per unit of time
Relationships between speed, distance, and time:
Speed = Distance/ Time = d/ t » Constant Speed- speed does not change over
time» Average Speed- speed of motion when speed
is changing
Avg Speed = Total Distance/ Total Time
» Instantaneous Speed- speed at any given moment in time (speedometer)
SpeedHow can we describe how fast an object moves?A car on Tolo Highway
travels 90 km in 1 hour. We say that the car travels at a speed of 90 km/h.
SpeedSpeed is a measure of how fast
something moves.
Speed = distance travelled per unit of time
Speed = distance travelled per unit of time
SI unit: m/s or km/h (for long distances)
How can we describe how fast an object moves?
KINDS OF SPEED
Average, Instantaneous, Constant
and speeds up again to 60 km/hand speeds up again to 60 km/h
Average speed
Its average speed over the whole journeyoverall distance travelled
total time of travel
slows down to 0 km/hslows down to 0 km/h
A car travels at 50 km/hA car travels at 50 km/h
=
Average speed does not tell the variations during the journey.
On most trips, the speed at any instant is often different from the
average speed.
Instantaneous speedspeed at any instant
The word ‘speed’ alone instantaneous speed
Instantaneous speed distance travelled in an extremely
short time interval
Simulation
Speedometer tells the car’s speed at any instant!
Instantaneous speed
Constant Speed Elapsed time
(seconds)Distance (meters)
0 0
2 4
4 8
6 12
8 16
10 20
12 24
Not changing
speed. Same
amount of speed from beginning
to last.
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
Graphing Motion
• Graph distance on the y-axis and time on the x-axis
Slope = rise = distance = speed run time
Distance - Time Graph
• If something is not moving, a horizontal line is drawn.
• If something starts out slow and then speeds up, its change in speed can look like this.
Learning Checkpoint
This graph shows several stages of motion:
• Stage 1: 100 m in 10 s
• Stage 2: 50 m in 10 s
• Stage 3: 150 m in 20 s
Calculate the speed as indicated by each of the colors.
Calculate the average speed.
What is the total distance?
What is the displacement?
Solution
Stage 1: S= d/ t100 m/ 10 s= 10 m/s
Stage 2: S= d/t50 m/ 10 s= 5 m/s
Stage 3: S= d/t150 m/ 20 s= 7.5 m/s
Ave Speed= Tot d/ Tot t300 m/ 40 s= 7.5 m/s
Distance = 300 metersDisplacement = 0 meters
KINDS OF VELOCITY
Average, Instantaneous, Constant
Velocity
rate of change of displacement. a speed in a given direction or
velocitya
vector quantit
y
direction
magnitude(speed)
Velocity is...
speed = 300 km/hdirection = west
Train drivers concern speed only.
Speed with direction
Pilots concern velocity (direction & speed).
speed = 90 km/h
Average velocity
Average velocity =overall displacement
total time of travel
direction of velocity = direction of overall displacement
Instantaneous velocity
The velocity at any instant is called instantaneous velocity.
If a car moves at a constant velocity...
… its average and instantaneous velocities have the same value.
Constant VELOCITYElapsed time
(seconds)Distance (meters)
0 0
2 4
4 8
6 12
8 16
10 20
12 24
Not changing
speed. Same
amount of speed from beginning
to last.
Graph: Constant VelocityDistance vs. Time
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30
Time
Dis
tan
ce
Velocity Time GraphElapsed
time (seconds)
Distance (meters)
Velocity (m/s)
0 0.0 0.0
2 4.0 2.0
4 8.0 2.0
6 12.0 2.0
8 16.0 2.0
10 20.0 2.0
12 24.0 2.0
Velocity vs Time
0
0.5
1
1.5
2
2.5
0 5 10 15
Time
Velo
city
Copy the data chart and construct a VELOCITY vs. TIME Graph
Terminal Velocity
Terminal velocity- the velocity at which the upward force of air resistance equals the downward force of gravity.
Once you reach this velocity you will no longer accelerate. (just stay at the same velocity)
Parachutes increase your surface area to increase your air resistance in order to reduce your terminal velocity so you don’t die when you hit the ground.
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.
Q1 The world record...
( )Average speed = 10.49
= 9.53 m/s or 34.3 km/h
100
The world record of women 100-m race is 10.49 s.
What is the average speed?
In an orienteering event, Maria and Karen reach their control points at the same time.
Q2 In an orienteering event...
start, 10:00 amstart, 10:00 amMaria, 10:30 amMaria, 10:30 am
Karen, 10:30 amKaren, 10:30 am
Who runs in a higher average velocity?Who runs in a higher average velocity?
A Maria.
B Karen.
C Undetermined since their paths are unknown.
D Incomparable since they run along different directions.
Who runs in a higher average velocity?Who runs in a higher average velocity?
Q2 In an orienteering event...
Note: The distance travelled is equal to magnitude of displacement only if it is a straight-line motion. Speed is usually larger than the magnitude of velocity.
Q3 True or false:
(T/F)
Average speed of an object magnitude of its average velocity.
A man takes a walk starting from rest and ending at rest.
Q4 True or false:
(T/F)
It is possible for him to attain an average speed of 5 km h–1 but he never goes faster than 5 km h–1.
ACCELERATION
Acceleration measures the change in velocity
Acceleration = velocity per unit time
Acceleration = velocity per unit time
direction
speed
overall change in velocitytotal time taken
= m/s2Unit: m/s / s vector quantity
=
AccelerationWhen a car moves faster and faster, its speed is increasing (velocity changed).
DEceleration
When a car moves slower and slower,
its speed is decreasing (- velocity changed).
When a car changes direction,
its velocity changes too.
Acceleration
• If you have starting and ending velocity or speed, find that before you use the triangle.
• If not, use triangle to find change in velocity (Dv), then find initial or final velocity
• Dv = ending velocity – starting velocity
Solving Acceleration Problems using Acceleration Triangle
a
Dv
t
If a car accelerates at 2 m/s, what does that mean?
3 Acceleration
t = 1 sv = 2 m/s,v = 2 m/s
v = 0
t = 2 sv = 4 m/s, v = 2 m/s
v = 6 m/s, v = 2 m/s
t = 3 s
1 m
t = 0
3 m
5 m
Acceleration at constant speed
• An object moving in a circle at constant speed is always
accelerating (changing direction).
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
Acceleration Questions
1) A dragster going at 10 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration?
2) The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 8 m/s in a time of 2 seconds. Find his acceleration.
3) Find the acceleration of a car that travels at a constant velocity of 40 Km/hr for 10 s.
4) Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 4 seconds down a ramp at an acceleration of 5 m/s2.
Uniform Acceleration : Velocity vs. Time
Velocity Time Graph: Uniform Acceleration
0
2
4
6
8
10
12
14
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Time
Vel
oci
ty
Elapsed time
(seconds)Distance (meters)
0.0 0
4.0 8
8.0 32
12.0 72
16.0 128
20.0 200
24.0 288
• What is the magnitude of the object’s total displacement after 4 seconds
• What is the average speed after 3 seconds?
Graph Question
8m
V= d/t
V= 8m/3s
V= 2.66 m/s
Summary• Distance and time measurements can be used to
describe the velocity and acceleration• The Shape of the Distance vs. Time determines the type of motion
– Rest : Straight line parallel to time axis– Constant Speed : Straight line on a slope (magnitude of the
speed)– Constant Acceleration: Curved line
• The Shape of the Velocity vs. Time determines the type of motion– Rest : Straight line on the time axis– Constant Speed : Straight line parallel to the Time axis– Constant Acceleration: Straight line on a slope (magnitude of the
Acceleration)
Q1 A running student...
A running student is slowing down in front of a teacher. With reference to the sign convention,
Acceleration of student: positive / negative
Velocity of student: positive / negative
+ve
Quantity Unit Scalar/Vector
Speed ______ _____
Velocity ______ _____
Change in velocity ______ _____
Acceleration ______ _____
Q2 When time is measured...
Unit of time: hour (h)
km h–1
km h–1
km h–1
km h–2
scalarvectorvectorvector
Unit of distance/displacement: kilometer (km)