Chapter 11 Motion Chapter 11 Motion 11.2 Speed 11.2 Speed and Velocity and Velocity
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Chapter 11 MotionChapter 11 Motion
11.2 Speed and 11.2 Speed and VelocityVelocity
StandardsStandards
SPS8a. Students will calculate SPS8a. Students will calculate velocity and accelerationvelocity and acceleration
Distance-Time GraphsDistance-Time Graphs
The distance traveled by The distance traveled by an object in a period of an object in a period of time often is expressed time often is expressed using a line graph. A line using a line graph. A line graph visually conveys graph visually conveys information using sets of information using sets of data points. data points.
Section 11.21.1. Copy the blank graph Copy the blank graph below on your paper. below on your paper. Complete the graph by Complete the graph by plotting the given data plotting the given data points on the graph. Each points on the graph. Each set of data points set of data points represents (time, distance). represents (time, distance). Note that time is Note that time is measured in seconds and measured in seconds and distance is measured in distance is measured in meters. Connect the meters. Connect the plotted points with a plotted points with a straight line. straight line.
Data points: (0, 0), (2, 40), Data points: (0, 0), (2, 40), (4, 80), (6, 120), (8, 160), (4, 80), (6, 120), (8, 160), (10, 200)(10, 200)
2.2. Describe the motion shown Describe the motion shown on the graph. on the graph.
Instantaneous speed vs Instantaneous speed vs average speedaverage speed
Average speedAverage speed is computed for is computed for the entire duration of a tripthe entire duration of a trip
Instantaneous speedInstantaneous speed is measured is measured at a particular instant. at a particular instant.
SpeedSpeed is the ratio of the distance an is the ratio of the distance an object moves to the amount of time object moves to the amount of time the object moves. the object moves.
–SI unit of speed is meters per SI unit of speed is meters per second (m/s). second (m/s).
time
distancespeed
Average SpeedAverage Speed
Average speedAverage speed, , is the total is the total distance traveled, distance traveled, d, d, divided by divided by the time, the time, t, t, it takes to travel that it takes to travel that distance. distance.
Calculating Average SpeedCalculating Average Speed
While traveling on vacation, you While traveling on vacation, you measure the times and measure the times and distances traveled. You travel distances traveled. You travel 35 kilometers in 0.4 hour, 35 kilometers in 0.4 hour, followed by 53 kilometers in 0.6 followed by 53 kilometers in 0.6 hour. What is your average hour. What is your average speed?speed?
1.1. A person jogs 4.0 kilometers in A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 22 minutes, and finally 1.0 kilometer in 16 minutes. What is kilometer in 16 minutes. What is the jogger’s average speed in the jogger’s average speed in kilometers per minute? kilometers per minute?
2.2. A train travels 190 kilometers in A train travels 190 kilometers in 3.0 hours, and then 120 kilometers 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average in 2.0 hours. What is its average speed? speed?
SpeedSpeed
3.3. At what speed did a plane fly if At what speed did a plane fly if it traveled 1760 meters in 8 it traveled 1760 meters in 8 seconds?seconds?
Instantaneous SpeedInstantaneous Speed
Instantaneous speedInstantaneous speed, , v, v, is the rate is the rate at which an object is moving at a at which an object is moving at a given moment in time. given moment in time.
Speed
How can you find the speed How can you find the speed from a distance-time graph? from a distance-time graph?
Graphing Motion
The The slopeslope of a line on a of a line on a distance-time graph is speed. distance-time graph is speed.
Graphing MotionGraphing Motion
slope =slope =
steeper slope =steeper slope =
straight line =straight line =
flat line =flat line =
Distance-Time Graph
A
Bfaster speed
constant speed
no motion
speed
E. Graphing SpeedE. Graphing Speed
Who started out Who started out faster?faster?
Who had a constant Who had a constant speed?speed?
Describe B from 10-Describe B from 10-20 min.20 min.
Find their average Find their average speeds.speeds.
Distance-Time Graph
A
B
Speed vs velocitySpeed vs velocity
VelocityVelocity is a description of is a description of both speed and direction of both speed and direction of motion. Velocity is a vector. motion. Velocity is a vector.
How do velocities add?How do velocities add?
Combining Velocities
Two or more velocities add Two or more velocities add by vector addition. by vector addition.
Velocity PracticeVelocity Practice1.1. A car travels 240 km in 3 hours. A car travels 240 km in 3 hours.
What is the speed?What is the speed?2.2. Find the velocity of a swimmer Find the velocity of a swimmer
who swims 110 m toward shore in who swims 110 m toward shore in 72 s.72 s.
3.3. Find the velocity of a baseball Find the velocity of a baseball thrown 38 m in 1.7 sthrown 38 m in 1.7 s
More Velocity PracticeMore Velocity Practice4. The speed of a cruise ship is 50 4. The speed of a cruise ship is 50
km/hr. How far will it travel in 14 km/hr. How far will it travel in 14 hours?hours?
5. Calculate the time in seconds an 5. Calculate the time in seconds an Olympic skier would take to finish Olympic skier would take to finish a 2600 m race at an average a 2600 m race at an average velocity of 28 m/s? velocity of 28 m/s?
Velocity ConnectionVelocity Connection
It is 2:00 PM. The weather bureau It is 2:00 PM. The weather bureau is tracking a violent storm traveling is tracking a violent storm traveling east at 25 km/hr. It is 75 km west east at 25 km/hr. It is 75 km west of Suntown. If everyone works of Suntown. If everyone works until 5:00 PM, will the residents of until 5:00 PM, will the residents of Suntown be able to get home Suntown be able to get home safely before the storm hits?safely before the storm hits?
Assessment Questions1.1. A woman jogs 10 kilometers in one A woman jogs 10 kilometers in one
hour, stops at a restaurant for one hour, stops at a restaurant for one hour, and then walks 10 kilometers in hour, and then walks 10 kilometers in two hours. What is her average speed two hours. What is her average speed for the outing? for the outing?
a.a. 0.2 km/h0.2 km/h
b.b. 4 km/h4 km/h
c.c. 5 km/h5 km/h
d.d. 10 km/h10 km/h
Assessment Questions
2.2. Lisa plotted time on the Lisa plotted time on the x-x-axis of a line axis of a line graph and distance on thegraph and distance on the y- y-axis. What axis. What does the slope of her graph represent?does the slope of her graph represent?a.a. total distance traveledtotal distance traveledb.b. velocityvelocityc.c. speedspeedd.d. displacementdisplacement
Assessment Questions
3.3. Lisa plotted time in seconds on the Lisa plotted time in seconds on the x-x-axis of a line graph and distance in axis of a line graph and distance in centimeters on thecentimeters on the y- y-axis. Her plot axis. Her plot showed a straight line from (0,0) to (10, showed a straight line from (0,0) to (10, 20). What is the speed? 20). What is the speed?
a.a. 0.5 cm/s0.5 cm/s
b.b. 2 cm/s2 cm/s
c.c. 10 cm/s10 cm/s
d.d. 20 cm/s20 cm/s
Assessment Questions
4.4. Two velocities of an object are Two velocities of an object are combined by using combined by using
a.a. division of the larger velocity by the division of the larger velocity by the smaller velocity.smaller velocity.
b.b. addition of the two speeds.addition of the two speeds.
c.c. vector addition.vector addition.
d.d. numeric addition.numeric addition.
Assessment Questions
5.5. A kayak is moving across a stream that A kayak is moving across a stream that is flowing downstream at a velocity of is flowing downstream at a velocity of 4 km/h. The kayak’s velocity is 3 km/h. 4 km/h. The kayak’s velocity is 3 km/h. What is the magnitude of the kayak’s What is the magnitude of the kayak’s velocity relative to the river bank? velocity relative to the river bank?
a.a. 1.3 km/h1.3 km/h
b.b. 5 km/h5 km/h
c.c. 7 km/h7 km/h
d.d. 12 km/h12 km/h
Assessment Questions
6.6.The SI unit for speed of an The SI unit for speed of an airplane is miles per hour.airplane is miles per hour.
TrueTrueFalseFalse
Assessment Questions3.3. If you were to sketch a displacement-time If you were to sketch a displacement-time
graph and a speed-time graph for an object graph and a speed-time graph for an object experiencing constant acceleration, what experiencing constant acceleration, what would they look like? would they look like?
a.a. Both graphs would be linear, with the Both graphs would be linear, with the displacement-time graph being steeper.displacement-time graph being steeper.
b.b. Both graphs would be linear, with the speed-Both graphs would be linear, with the speed-time graph being steeper.time graph being steeper.
c.c. Both graphs would be nonlinear.Both graphs would be nonlinear.
d.d. The speed-time graph would be linear; the The speed-time graph would be linear; the displacement-time graph would be displacement-time graph would be nonlinear.nonlinear.
Assessment Questions
6.6. If an object experiences a steady If an object experiences a steady velocity change in a straight line, it velocity change in a straight line, it is undergoing constant is undergoing constant acceleration.acceleration.
TrueTrueFalseFalse
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