Download Ch 2 outline - Huber Heights City Schools

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Linear Motion Outline
Physics Chapter 2
I.
Displacement and Velocity
A. Describe what linear motion is and give an example.
B. Frame of reference:
C. Displacement:
Displacement
D. Why is displacement not always equal to the distance traveled?
E. Which ways are usually positive and negative when dealing with motion?
F. Average velocity:
Average velocity
Example 1: During a race on level ground, Andrea runs with an average velocity of 6.02 m/s to the east.
What distance does Andrea cover in 137 s?
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Example 2: A child is pushing a shopping cart at a speed of 1.5 m/s. How long will it take this child to
push the cart down an aisle with a length of 9.3 m?
G. What is the difference between velocity and speed?
H. Instantaneous velocity:
Practice Set 2A
1. Describe the difference between instantaneous velocity and average velocity.
2. Heather and Matthew walk eastward with a speed of 0.98 m/s. If it takes them 34 minutes to walk to
the store, how far have they walked?
3. If Joe rides south on his bicycle in a straight line for 15 minutes with an average speed of 12.5 m/s,
how far has he ridden?
4. It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to
the museum entrance. What is your displacement?
5. Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to
drive 144 km on a straight highway?
6. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south.
The bus stops for 24 minutes, then it travels 210 km south with an average velocity of 75 km/h to the
south.
a. How long does the total trip last?
b. What is the average velocity for the total trip?
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II.
Acceleration
A. Acceleration
Average Acceleration
Example 3: A shuttle bus slows to a stop with an average acceleration of –1.8 m/s2. How long does it
take the bus to slow from 9.0 m/s to 0.0 m/s?
Example 4: Find the acceleration of an amusement park ride that falls from rest to a speed of 28 m/s in
3.0 s.
Practice Set 2B
1. A bowling ball with a negative initial velocity slows down as it rolls down the lane toward the pins. Is
the bowling ball’s acceleration positive or negative?
2. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at -4.1 m/s2
as it slows from 9.0 m/s to 0 m/s. Find the time interval of acceleration for the bus.
3. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s2 to reach a speed of 12.0 m/s. How long
does it take for this acceleration to occur?
4. With an average acceleration of -0.50 m/s2, how long will it take a cyclist to bring a bicycle with an
initial speed of 13.5 m/s to a complete stop?
5. A race car’s velocity increases from 4.0 m/s to 36 m/s over a 4.0 s time interval. What is its average
acceleration?
6. Turner’s treadmill runs with a velocity of -1.2 m/s and speeds up at regular intervals during a halfhour workout. After 25 minutes, the treadmill has a velocity of -6.5 m/s. What is the average
acceleration of the treadmill during this period?
7. If a treadmill has an initial speed of 1.7 m/s and an average acceleration of 4.7 x 10-3 m/s2, what will
its final speed be after 5.0 minutes?
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B. How can the acceleration of an object be positive or negative?
C. Is this correct: when velocity is zero, acceleration has to be zero; and when acceleration is
zero velocity has to be zero?
D. Motion with Constant Acceleration
Displacement with Constant Uniform Acceleration
Example 5: A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration,
using its parachute and braking system, and comes to rest 5.5 s later. Find how far the car moves
while stopping.
Example 6: A bicyclist travels a distance of 84.0 m while accelerating from a beginning velocity of
5.0 m/s for 8 s. Assuming uniform acceleration, what is the final velocity of the bicyclist?
Practice Set 2C
1.Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the
instantaneous velocity of car A exceeds the instantaneous velocity of car B. Does this mean that car A’s
acceleration is greater than car B’s? Explain.
2. A car accelerates uniformly from rest to a speed of 6.58 m/s in 6.5 s. Find the distance the car travels
during this time.
3. When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0 m/s in 2.50 s.
How many meters before the stop sign must she apply her brakes in order to stop at the sign?
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4. A jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s2
as it comes to rest. Can this plane land on a runway at an airport where the runway is 0.80 km long?
5. A driver in a car traveling at a speed of 21.67 m/s sees a cat 101 m away on the road. How long will it
take for the car to accelerate uniformly to a stop in 99 m?
6. A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 minutes.
How fast is the car moving after this time?
Velocity with Constant Uniform Acceleration
Displacement with Constant Uniform Acceleration
Example 7: A plane starting at rest at one end of the runway undergoes a uniform acceleration of 4.8 m/s2
for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be
able to take off?
Example 8: A boy sledding down a hill accelerates at 1.40 m/s2. If he started from rest, in what distance
would he reach a speed of 7.00 m/s?
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Practice Set 2D
1. A car with an initial speed of 6.58 m/s accelerates at a uniform rate of 0.92 m/s2 for 3.6 s. Find the
final speed and the displacement of the car during this time.
2. An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the
final speed AND the displacement after 5.0 s.
3. A car starts from rest and travels for 5.0 s with a uniform acceleration of -1.5 m/s2.
a. What is the final velocity of the car?
b. How far does the car travel in this time interval?
4. A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of -2.0 m/s2.
a. How long does it take the car to accelerate to a final speed of 10.0 m/s?
b. How far has the car moved during the braking period?
5. A bus that is traveling at 30.0 km/h speeds up at a constant rate of 3.5 m/s2. What velocity does it
reach 6.8 s later?
6. A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s2. How many seconds are required
before the car is traveling at 3.0 m/s?
Final Velocity After Any Displacement
Example 9: A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2.
What is the velocity of the stroller after it has traveled 4.75 m?
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Name_________________________ Pd. _____
Example 10: An aircraft has a landing speed of 302 km/h. The landing area of an aircraft carrier is 195 m
long. What is the minimum uniform acceleration required for a safe landing?
Practice Set 2E
1. A car traveling at 7.0 m/s accelerates uniformly at the rate of 0.80 m/s2 for a distance of 245 m.
a. What is the velocity at the end of the acceleration?
b. What is the velocity after it accelerates for 125 m?
c. What is the velocity after it accelerates for 67 m?
2. A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s2.
a. What is the speed of the car after it has traveled 55 m?
b. How long does it take the car to travel 55 m?
3. A certain car is capable of accelerating at a uniform rate of 0.85 m/s2. What is the car’s displacement
as it accelerates from a speed of 23.1 m/s to one of 26.1 m/s?
4. An aircraft has a liftoff speed of 120 km/h. What minimum uniform acceleration does this require if
the aircraft is to be airborne after a take-off run of 240 m?
5. A motorboat accelerates from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If
its acceleration was 2.7 m/s2 to the east, how far did it travel during the acceleration?
6. A man runs at a velocity of 4.5 m/s for 15.0 minutes. Then he goes up an increasingly steep hill and
slows down at a constant rate of 0.05 m/s2 for 90.0 s and comes to a stop. How far, in total did he
run?
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Name_________________________ Pd. _____
IV. Falling Objects
A. Free-fall:
B. What is the free-fall acceleration?
Example 11: Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If
the volleyball starts from 2.0 m above the floor, how long will it be in the air before it strikes the floor?
Assume Jason is the last player to touch the ball before it hits the floor.
Example 12: A ball is thrown straight up into the air at an initial velocity of 25.0 m/s. Create a table
showing the ball’s position, velocity, and acceleration for the first two seconds of its motion.
Practice Set 2F
1. A coin is tossed vertically upward.
a. What happens to its velocity while it is in the air?
b. Does its acceleration increase, decrease, or remain constant while it is in the air?
2. A ball is thrown vertically upward. What are its velocity and acceleration when it reaches it
maximum altitude? What is its acceleration just before it hits the ground?
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3. A robot probe drops a camera off the rim of a 239 m high cliff on Mars, where the free-fall
acceleration is -3.7 m/s2.
a. Find the velocity with which the camera hits the ground.
b. Find the time required for it to hit the ground.
4. A flowerpot falls from a windowsill 25.0 m above the sidewalk.
a. How fast is the flowerpot moving when it strikes the ground?
b. How much time does a passerby on the sidewalk below have to move out of the way before
the flowerpot hits the ground?
5. A tennis ball is thrown vertically upward with an initial velocity of 8.0 m/s.
a. What will the ball’s speed be when it returns to its starting point?
b. How long will the ball take to reach its starting point?
6. Stephanie hits a volleyball from a height of 0.80 m and gives it an initial velocity of 7.5 m/s straight
up.
a. How high will the volleyball go?
b. How long will it take the ball to reach it maximum height?
7. Maria throws an apple upward from a height of 1.3 m with an initial velocity of 8.4 m/s. Will the
apple reach a friend in a treehouse 5.3 m above the ground?
8. You decide to flip a coin to determine whether to do your physics homework. The coin is flipped
straight up.
a. If the coin reaches a high point of 0.25 m above where you released it, what was its initial
speed?
b. If you catch it at the same height as you released it, how much time did it spend in the air?
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