Distance and Displacement 11.1
To describe motion, you must state the _____________ the object is moving as well as how _____________ the
object is _____________.
You must also tell its _____________ at a certain _____________.
What is needed to describe motion completely?
A _____________ of _____________ is a system of objects that are not moving with respect to one another.
How Fast Are You Moving?
How fast the passengers on a train are moving depends on the frame of reference chosen to measure their motion.
Relative motion is movement in _____________ to a _____________ of reference.
•As the train moves past a platform, people standing on the platform will see those on the train
_________________ by.
•When the people on the train look at one another, they don’t seem to be moving at all.
To someone riding on a speeding train, others on the train don’t seem to be moving.
Which Frame Should You Choose?
•When you sit on a train and look out a window, a treetop may help you see how ___________ you are
_________________ relative to the _________________.
•If you get up and ______________ toward the rear of the train, looking at a seat or the floor shows how
_________________ you are walking _________________ to the train.
•Choosing a _________________ frame of reference allows you to _________________ motion in a clear and
_________________ manner.
Distance and displacement are different.
Distance is the _________________ of a path between two points.
When an object moves in a straight line, the _________________ is the _________________ of the line
_________________ the object’s starting point and its ending point.
•The SI unit for measuring distance is the _________________ (m).
•For very large distances, it is more common to make measurements in _________________ (km).
•Distances that are smaller than a meter are measured in _________________ (cm).
To describe an object’s _________________ relative to a given _________________, you need to know how far
away _______ in what _________________ the object is from that point.
_____________________provides this information.
Think about the motion of a roller coaster car.
•The _________________ of the path along which the car has _________________ is _________________.
•Displacement is the length of a straight line drawn from the starting point of the car to its stopping point.
•After completing a trip around the track, the car’s displacement is ____________.
How do you add displacements?
A _________________ is a quantity that has magnitude and direction.
_________________ is an example of a _________________.
•The _________________ can be size, length, or amount.
•Arrows on a graph or map are used to represent vectors. The _________________ of the arrow shows the
_________________ of the vector.
•Vector addition is the _________________ of vector magnitudes and directions.
Displacement Along a Straight Line
When two displacements, represented by two vectors, have the same direction, you can ________ their magnitudes.
•Add the magnitudes of two displacement vectors that have the same direction.
____________________________________________________________________
0
1
2
3
4
5
6
•Two displacement vectors with opposite directions are subtracted from each other.
____________________________________________________________________
0
1
2
3
4
5
6
Displacement That Isn’t Along a Straight Path
When two or more displacement vectors have _______________ directions, they may be combined by
_______________.
Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy’s home to his school
is two blocks less than the distance he actually traveled.
The boy walked a total distance of 7 blocks.
This is the _________ of the magnitudes of each vector along the path.
The vector in red is called the resultant vector, which is the vector sum of two or more vectors.
The resultant vector points _______________from the starting point to the ending point.
1. A car is driving down the highway. From which frame of
3. if you walk across town, taking many turns, your displacement is
reference does it appear to not be moving?
the
A)
standing at the side of the road
A)
total distance that you traveled.
B)
a car driving at the same speed but going the opposite
B)
distance and direction of a straight line from your starting
C)
sitting inside the car
D)
an airplane flying overhead
direction
point to your ending point.
C)
distance in a straight line from your starting point to your
ending point.
D)
direction from your starting point to your ending point.
2. The SI unit of distance that would be most appropriate for
4. You travel 30 km west of your home and then turn around and
measuring the distance between two cities is the
start going back home. After traveling 10 km east, what is your
A)
meter.
displacement from your home?
B)
centimeter.
A)
20 km
C)
kilometer.
B)
20 km west
D)
mile.
C)
40 km
D)
40 km west
Speed and Velocity 11.2
The _________________ of an in-line skater is usually described in _________________ per second.
The _________________ of a car is usually described in kilometers per _________________.
_________________ is the _________________ of the _________________ an object moves to the amount of
_________________ the object moves.
The SI unit of speed is _________________ per _________________ (m/s).
Two ways to express the speed of an object are average speed and instantaneous speed.
How are instantaneous speed and average speed different?
Average Speed
Sometimes it is useful to know how fast something _________________ for an _________________ trip, even
though its speed may change _________________ the trip.
_________________ speed, is the _________________ distance traveled, d, _________________ by the
_________________, t, it takes to travel that distance.
Calculating Average Speed
While traveling on vacation, you measure the times and distances traveled. You travel 35 kilometers in 0.4 hour,
followed by 53 kilometers in 0.6 hour. What is your average speed?
1. A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometer in 16
minutes. What is the jogger’s average speed in kilometers per minute?
2. A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its average speed?
Instantaneous Speed
Sometimes you need to know how fast you are going at a particular _________________.
_________________ speed, v, is the _________________ at which an object is _________________ at a given
_________________ in time.
The _________________ in a car measures the car’s _________________ speed.
Note the scale markings are given both in km/h and miles per hour, mph.
How can you find the speed from a distance-time graph?
A distance-time _________________ is a good way to _________________ motion.
Slope is the _________________ in the vertical axis value divided by the change in the _________________ axis
value.
A _________________ slope on a distance-time graph indicates a higher _________________.
How are speed and velocity different?
Sometimes knowing only the _________________ of an object isn’t _________________.
You also need to know the _________________ of the _________________ motion.
Together, the _________________ and _________________ in which an object is _________________ are called
velocity.
A cheetah’s _________________ may be as fast as 90 km/h.
To describe the cheetah’s _________________, you must also know the _________________ in which it is
_________________.
Vectors can be used to show changes in motion.
•Vectors of varying lengths, each vector corresponding to the velocity at a particular instant, can represent
motion.
•A longer vector represents a faster speed, and a shorter one a slower speed.
•Vectors point in different directions to represent direction at any moment.
As the sailboat’s direction changes, its velocity also changes, even if its speed stays the same.
How do velocities add?
Sometimes the motion of an object involves more than one _________________.
If a boat is moving on a _________________ river, the velocity of the river relative to the riverbank and the velocity
of the boat relative to the river _________________.
They _________________ the velocity of the ______________ relative to the ___________________.
The velocity of the boat relative to the riverbank is a combination of the relative velocities of the boat and the river.
1. A woman jogs 10 kilometers in one hour, stops at a restaurant for one hour, and then walks 10 kilometers in two
hours. What is her average speed for the outing?
A) 0.2 km/h
B) 4 km/h
C) 5 km/h
D) 10 km/h
2. Lisa plotted time on the x-axis of a line graph and distance on the y-axis. What does the slope of her graph
represent?
A) total distance traveled
B) velocity
C) speed
D) displacement
3. Lisa plotted time in seconds on the x-axis of a line graph and distance in centimeters on the y-axis. Her plot
showed a straight line from (0,0) to (10, 20). What is the speed?
A) 0.5 cm/s
B) 2 cm/s
C) 10 cm/s
D) 20 cm/s
4. Two velocities of an object are combined by using
A) division of the larger velocity by the smaller velocity.
B) addition of the two speeds.
C) vector addition.
D) numeric addition.
5. A kayak is moving across a stream that is flowing downstream at a velocity of 4 km/h. The kayak’s velocity is
3 km/h. What is the magnitude of the kayak’s velocity relative to the river bank?
A) 1.3 km/h
B) 5 km/h
C) 7 km/h
D) 12 km/h
Acceleration 11.3
The basketball ________________changes velocity as it rises and falls.
Describing ________________ in ________________, and how fast they occur, is a part of describing motion.
How are changes in velocity described?
The ___________at which ________________changes is called ________________.
Changes in Speed
•In science, ________________applies to __________change in an object’s ________________.
•Acceleration can be caused by ________________ (increasing) change in ________________or by negative
(decreasing) ________________in speed.
•________________is an acceleration that ______________an object’s speed.
Free fall is the ________________of an object toward ________________solely because of ________________.
The ________________for velocity is ________________per ________________.
The unit for acceleration, then, is meters per second ________
________________.
This unit is ________________written as ________________per __________________
______________
2
(m/s ).
Objects ________________near Earth’s ________________accelerate downward at a rate of _____________.
Each ________________an object is in free fall, its ________________increases downward by ______meters per
second.
2
The change in the stone’s speed is 9.8 m/s , the ________________due to ________________.
Changes in Direction
________________can be the result of a ________________in direction at constant speed, for example, riding a
bicycle around a curve.
A horse on the carousel is traveling at a ________________speed, but it is ________________because its
________________is ________________changing.
Changes in Speed and Direction
Sometimes ________________is characterized by changes in both ________________and ________________at
the same time.
Passengers in a car moving along a ________________road experience ________________changing
________________.
The car may enter a long ________________at the same time that it ____________.
The car is ________________both because it is changing ________________and because its speed is
________________.
A roller coaster produces acceleration due to changes in __________speed and direction.
Constant Acceleration
The ________________of an object moving in a straight line changes at a constant rate when the object is
experiencing ________________acceleration.
•Constant acceleration is a ________________change in ________________.
•An airplane’s ________________may be ________________during a portion of its takeoff.
Constant acceleration during ________________results in changes to an aircraft’s ________________that is in a
________________direction.
How can you calculate acceleration?
Acceleration is the rate at which velocity changes. Vi is the initial velocity, vf is the final velocity, and t is total time.
If the velocity ________________, the acceleration is ________________.
If the velocity ________________, the acceleration is ________________.
•If you are coasting downhill on a bicycle, your velocity increases, and your acceleration is positive.
•If you continue coasting on level ground, your velocity decreases, and your acceleration is negative.
Acceleration and velocity are both _________________
_______________.
•To determine a ________________in ________________, subtract one velocity vector from
________________.
•If the motion is in a ________________line, velocity can be treated as ________________, and
________________is the change in ________________divided by the __________.
Calculating Acceleration
A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the
acceleration of the ball?
What information are we given?
What unknown are you trying to calculate?
What formula contains the given quantities and the unknown?
Put in the given values and calculate the unknown.
1. A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its
acceleration?
2
2. An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s . What is its change in velocity
during this time?
3. A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the
velocity of the ball when it strikes the water?
4. A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was
the rock going when it left the boy’s hand?
How does a speed-time graph indicate acceleration?
You can use a graph to calculate acceleration.
Graph speed on the ________________axis and time on the ________________axis.
The slope is change in speed ________________by change in time, which is equal to the ________________.
Speed-Time Graphs
________________acceleration is represented on a speed–time graph by a ________________line.
The ________________of the line is the acceleration.
The graph is an example of a linear graph, in which the displayed data form straight-line parts.
Constant negative acceleration ________________speed.
•On a speed-time graph of a bicycle slowing to a stop, a line sloping ________________represents the bicycle
________________.
•The change in speed is ________________, so the slope of the line is ________________.
Distance-Time Graphs
Accelerated motion is represented by a curved line on a distance-time graph.
In a nonlinear graph, a curve connects the data points that are plotted.
A distance-time graph of accelerated motion is a curve.
The data in this graph are for a ball dropped from rest toward the ground.
Compare the ________________of the curve during the first ________________to the slope during the fourth
second. An increasing slope means that the speed is ________________.
What is instantaneous acceleration?
Acceleration is ________________constant, and motion is rarely in a ________________line.
•Acceleration involves a change in velocity or direction or both, so the vector of acceleration can point in
_______direction.
•The vector’s length depends on how fast velocity is changing.
•For an object that is standing still, the acceleration vector is zero.
1. What is acceleration?
A)
the rate at which speed increases
B)
the time an object’s velocity increases
C) the rate at which displacement changes
D) the rate at which velocity changes
2. What is the SI unit for acceleration?
A)
m/s
B)
s /m
2
C) m/s
2
D) s/m
3. A sports car can accelerate from 0 m/s to 28 m/s in four seconds. What is the acceleration of the car?
A)
24 s
B)
7 m/s
2
C) 27 m/s
D) 27 m/s
2
4. If you were to sketch a displacement-time graph and a speed-time graph for an object experiencing constant acceleration,
what would they look like?
A)
Both graphs would be linear, with the displacement-time graph being steeper.
B)
Both graphs would be linear, with the speed-time graph being steeper.
C) Both graphs would be nonlinear.
D) The speed-time graph would be linear; the displacement-time graph would be nonlinear.
5. Which of the following is an example of negative acceleration?
A)
Mike starts riding his bike and uses the pedals to go from 0 km/h to 20 km/h.
B)
Mike pedals up a hill and gradually slows from 20 km/h to 5 km/h.
C) Mike sits on his bike at the top of the hill and rests.
D) Mike coasts downhill without pedalling, going from 0 km/h to 15 km/h.
6. The acceleration at a specific point on a distance-time graph is the
A)
instantaneous acceleration.
B)
momentary acceleration.
C) positive acceleration.
D) numerical acceleration.