# Motion in One Dimension (One Dimensional...

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1

Motion in One Dimension (One Dimensional Kinematics)

Position (x) : Initial Position Final Position Change in Position

Distance (d): Displacement (Δx or d):

I.

II.

Initial Position Final Position Change in Position Displacement Distance

Initial Position Final Position Change in Position Displacement Distance

III.

Essential idea: Motion may be described and analysed by the use of graphs and equations.

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2

Speed and Velocity

I.

Velocity (v) :

Speed (v) :

II.

1. If a person is moving in the positive direction, she has a . . . . 2. If a person is moving in the negative direction, he has a . . .

Speed = Velocity =

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1. What does the slope of the position-time graph represent?

The following shows a car moving at a constant speed.

2. What does the area under the velocity-time graph represent?

Time (s) 0 1 2 3 4

Displacement (m)

Velocity (m/s)

A student runs from home to school and back.

Magnitude: Scalar:

Examples of scalar quantities: Vector: Examples of vector quantities:

3. When is the distance an object travels equal to its displacement (in magnitude)? 4. When is the speed of an object equal to its velocity (in magnitude)? 5. How can you drive at a constant speed but not at a constant velocity?

Running from home to school Round trip

Distance

Displacement

Speed

Velocity

Essential idea: Some quantities have direction and magnitude, others have magnitude only, and this understanding is the key to correct manipulation of quantities

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Average vs. Instantaneous

Calculate your speed for a trip to Safeway.

Time (s)

Sp

eed

(m

/s)

Sketch a graph of your speed for your trip.

3. Describe a trip in which a car’s average speed equals its instantaneous speed for the entire time.

1. Average speed (or velocity):

2. Instantaneous speed (or velocity):

Problem Solving –Smooth Form

solution with

units

4. An airplane flies at a constant speed of 300. m/s. How long will it take the plane to fly a distance of 1.2 km?

5. A car travels at an average speed of 30. m/s. How far will the car go in 3.0 hours?

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Acceleration

A cart is allowed to roll freely down a ramp, as shown below. The position of the cart is marked after each second.

1. Describe the distance the cart travels each second.

2. Describe any changes in the speed and velocity of the cart as it rolls downhill.

Time

(s) Position (m)

Average Velocity

(m/s)

Instantaneous Velocity

(m/s)

Acceleration

0

1

2

3

4

Instantaneous initial velocity =

Instantaneous final velocity =

Average velocity =

Acceleration:

Formula: Units:

Type:

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3. Use the chart you just filled in to sketch the following graphs of motion for the cart.

4. What is the relationship between position and time?

5. What is the relationship between velocity and time?

6. What is the relationship between acceleration and time?

Uniform acceleration:

9. What is the meaning of the slope of the position-time graph?

7. What is the meaning of the slope of the velocity-time graph?

8. What is the meaning of the area under the velocity-time graph?

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Graphs of Accelerated Motion

Sketch below your predictions and the results for the fan-cart moving away from the detector and speeding up at a steady rate.

RESULTS

PREDICTION

DEMO #1

1. What is the significance of the slope of the velocity-time graph?

Sketch below your predictions and the results for the fan-cart moving away from the detector and slowing down at a steady rate.

RESULTS

PREDICTION

DEMO #2

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Sketch below your predictions and the results for the fan-cart moving towards the detector and speeding up at a steady rate.

RESULTS

PREDICTION

DEMO #3

Sketch below your predictions and the results for the fan-cart moving towards the detector and slowing down at a steady rate.

RESULTS

PREDICTION

DEMO #4

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deceleration:

2. Complete the following chart by looking back over the four demos to determine which carts:

3. What does it mean for the cart to have a positive velocity?

4. What does it mean for the cart to have a negative velocity?

Were

moving in

a positive

direction

Were

moving in

a negative

direction

Had a

positive

velocity

Had a

negative

velocity

Were

speeding

up

Were

slowing

down

Had a

positive

acceleration

Had a

negative

acceleration

5. What does it mean for the cart to have a positive acceleration?

6. If the cart has a positive acceleration, does it have to be speeding up (going faster)?

7. What does it mean for the cart to have a negative acceleration?

8. If the cart has a negative acceleration, does it have to be slowing down (going slower)?

9. In each case below, decide whether the car is speeding up or slowing down.

10. Compare the car’s velocity and its acceleration when it is speeding up.

11. Compare the car’s velocity and its acceleration when it is slowing down.

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Acceleration

Acceleration:

Formula:

Units:

Type:

1. Calculate the acceleration of the plane.

2. Calculate the acceleration of the racecar.

If an object has a negative acceleration, does that mean it is decelerating?

negative acceleration:

3. Calculate the acceleration of the plane.

Can an object have a negative acceleration and be speeding up?

1. What are the three ways an object can accelerate?

a) b) c)

2. Can a car have a constant speed and be accelerating?

3. Can a car have a constant velocity and be accelerating?

4. Is it possible for a car to have velocity but no acceleration? Explain and give an example.

5. Is it possible for a car to have acceleration but no velocity? Explain and give an example.

Turning

HON

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BIG 3

Kinematics Equations

6. A motorcycle traveling at 12.6 m/s accelerates at a rate of 1.7 m/s2 for 3.4 seconds. What is its final velocity? Vf = vi + at Vf = 12.6 m/s + (1.7 m/s2 )(3.4 s) Vf = 18.38 m/s Vf = 18 m/s

7. A bullet is accelerated from rest at a rate of 400 m/s2 for 0.05 seconds. How far did it travel while it was accelerating?

8. An elephant accelerates from 5.0 m/s to 10. m/s at a rate of 2.0 m/s2. What is the elephant's final displacement?

D = vit + ½ a t2 D = 0 + ½ (400 m/s2)(.05s)2 D = 0.5 m

Vf2 = vi2 + 2ad (10. m/s)2 = (5.0 m/s)2 + 2(2.0 m/s2)d D = 18.75 m D = 19 m

9. A driver brings a car traveling at 22 m/s to a full stop in 4.0 seconds.

a) What is the car's acceleration?

b) How far did the car travel before stopping?

A = Δv/t A = (0 – 22 m/s)/4.0 s A = -5.5 m/s2

HON

13

V bar = d/t

11. Skid marks left from a stopped car are 27 meters long. If the car had a deceleration of 6.0 m/s2 and stopped in 3.0 seconds, how fast was the car moving initially?

11. Starting with a velocity of 2.0 m/s, a lion moves 110 m in 5.0 seconds. What was the lion’s acceleration?

D = vit + ½ at2 27 m = vi(3.0 s) + ½ (-6.0 m/s2)(3.0 s)2 Vi = 18 m/s

D = vit + ½ at2 A = (d-vit)/ ½ t2 A = (110-2.0m/s * 5.0s)/( ½ (5.0 s)2) A = 8.0 m/s2

12. In a historical movie, two knights on horseback start from rest 88.0 m apart and ride directly toward each other to do battle. Sir George’s acceleration has a magnitude of 0.300 m/s2, while Sir Alfred’s has a magnitude of 0.200 m/s2. Relative to Sir George’s starting point, where do the knights collide?

13

Video 1 Video 2 Video 3

Observations:

Observations:

Observations:

Air Resistance Gravity

Earth

Moon

Deep Space

Free-Fall and Gravity

Describe the motion of a falling object.

The Law of Falling Bodies:

Freely falling:

Compare the following locations.

Acceleration due to Gravity

1.

2.

3.

4.

Selected Values of “g”

Eugene g =

Equator g =

North Pole g =

Moon g =

Mars g =

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Complete the chart for the displacement, instantaneous velocity and acceleration of the ball.

time (s) d (m) v (m/s) a (m/s2)

0

1

2

3

4

5

Sketch the position, velocity and acceleration graphs for the falling ball. How would these change if

distance and speed were graphed instead?

1. A ball is dropped down a shaft and hits the

bottom in 3.2 seconds. Determine:

a) the depth of the shaft

b) how fast the ball is going when it hits the

bottom

2. A stunt man jumps off the Brooklyn Bridge which is

40. meters high. Determine:

a) the time it takes to hit the water

b) his impact velocity

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Throwing Up

A ball is thrown up into the air, as shown in the time-elapsed diagram. Each snapshot

represents the position of the ball after one additional second of flight.

a) How long is it in the air?

b) How long did it take to get to the top of its path?

c) How fast was it going when it left the ground?

d) Describe how its speed changes during the flight.

e) Describe how its velocity changes during the flight.

f) Describe how its acceleration changes during the flight.

Position (m) Velocity (m/s) Acceleration

(m/s2)

A

B

C

D

E

F

G

g) Sketch vectors on the diagram to

indicate the velocity and acceleration of

the ball at each instant.

h) Complete the chart at right for the ball.

i) Sketch the graphs below for the ball.

16

1. A football is punted straight up and remains airborne for 2.6 seconds. Determine:

a) the time it takes to get to the top of its flight

b) vertical launching velocity

c) highest point reached

2. A ball is thrown straight up in the air with an initial velocity of 15 m/s. Determine:

a) the time it takes to get to the top of its flight

b) highest point reached

c) impact velocity