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MOTIONIN ONE DIMENSION.

VELOCITY AND ACCELERATION

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Reference point

• Frame of reference. Used to define motion.

• Is your desk in motion?

• Is the room in motion?

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• Position (d)—separation between an object and a reference point. Shows both distance and direction.

• Distance (d)—needs no reference frame. The measurement of separation of 2 objects. (how far)

• Displacement (d)—change in position. Shows both distance and direction.

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• -2 -1 0 1 2 3 4 5 6 7 8 9 (number line)(zero is the reference point)**we can make any number the ref pt.

• Point A is 8m to the right of zero. +8m

• Point B is 1 m to the left of zero. -1m

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Scalar vs. vector

• Scalar—quantity—has only magnitude or size

• Examples 1. Mass2. Leaves on a tree3. Time4. Distance5. Speed

• Vector—shows magnitude and direction. (shown with an arrow—points the direction)

Examples 1. Position 2. Displacement3. Velocity4. Acceleration5. Force6. Weight

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Displacement

• Change in position of an object.

• Δd = d2 – d1

• A vector quantity

• Tells magnitude and direction

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• If you go from your house to your friends house and then to the store? What distance did you travel? What is your displacement?

• If you return to your house, what total distance did you travel? What is your displacement?

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Rules for problem solving• Always make columns---not rows.• Read the entire problem.• Write the given number and units.• Decide what the unknown is.• Decide which formula to use and write it down. This is the BASIC

equation.• Transpose or manipulate the basic equation for the unknown. This

is the WORKING equation.• Substitute given values and units, writing ALL significant figures.• Do dimensional analysis (check your units)• Do all calculations at one time and write the calculator value down.• Round your answer using the significant figure rules.• Check your answers for reasonableness.

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Velocity and acceleration video

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Convert the 100 km/h to m/s

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A person runs a 100.0m race in 10.54 sec. What is the average

velocity in m/s & km/h?

• Given• d = 100.0 m

t = 10.54 sec v = ?

• v = d/t• v = 100.0 m/10.54s

• v = 9.487666034•

v = 9.488 m/s

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Practice problems

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Constant velocity with a position time graph

• The ratio Δd/Δt is constant• Slope of the line represents velocity.• v = d/t• What type of graph is this? What is the

relationship?

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CALCULATING THE SLOPE OF A LINE.

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Position-time graph

• Which object(s) is(are) maintaining a state of motion (i.e., maintaining a constant velocity)?

• Which object(s) is(are) accelerating?

• Which object(s) is(are) not moving?

• Which object(s) change(s) its direction?

• Which object is traveling fastest? Which moving object is traveling slowest?

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Calculate the average velocity

• Find the slope of the line.

• Δv = Δd/Δt• v = 50m – 0m/5s – 0s• v = 50m / 5s• v = 10 m/s

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• Which object(s) is(are) maintaining its state of motion?

• Which object(s) is(are) accelerating?

• Which object(s) is(are) not moving?

• Which object(s) change(s) its direction?

• A & E

• B & C (D during the 1st part)

• All objects are moving

• B & C

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• How can you find the displacement using a velocity-time graph?

• Calculate the area under the curve (bh) or ½(bh)

• How can you find acceleration using a velocity-time graph?

• **hint** a = v/t

• Calculate the slope of the line

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Velocity-time graph

• Find displacement by finding the area under the curve. d = vt

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Acceleration

• Change in velocity

• Vector quantity

• m/s/s or m/s2

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1. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study

each car individually in order to determine the answer.

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Consider the position-time graph at the right. Each one of the three lines on the position-time graph corresponds to the motion of one of the three cars. Match the appropriate

line to the particular color of car.

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Uniform acceleration equations

• vf = vi + at

• d = ½ (vf + vi)t

• d = vit + ½ at2

• vf2 = vi

2 + 2ad

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For practice

1. What is the displacement of a train as it accelerates from 11 m/s to 33 m/s in a 20.0 s interval?

2. If a car w/a velocity of 2.0 m/s at t = 0 accelerates at a rate of 4.0 m/s2 for 2.5 s, what is its velocity?

3. An airplane must reach a velocity of 71 m/s for take-off. If the runway is 1.0 km long, what must the constant acceleration be?

4. A car starts from rest, accelerates uniformly at 6.10 m/s2 for 7.0 s. How far does the car travel?

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• Draw a position-time graph and a velocity-time graph for the following motion.

• You walk to a friends house at a constant speed, stop to talk for a while, then run home at a steady speed.

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Speed and acceleration video

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ACCELERATON DUE TO GRAVITY

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Why do the 2 objects of the left fall at the same rate and the 2 objects

on the right don’t?

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ACCELERATION DUE TO GRAVITY

• We know that no matter what the mass of the object is, whether it’s dropped from 1 m, 10m or 100m, thrown or dropped, as long as air resistance is ignored, the acceleration due to gravity “g” is the same for all objects at the same location of Earth.

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Acceleration due to gravity

• Symbol-- g

• Units—m/s2

• Value on Earth -9.81 m/s2

• Vector quantity (shows magnitude and direction)

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EQUATIONS

• Vf = vi + gt

• Vf2 = vi

2 + 2gd

• d = vit + 1/2gt2

• Compare these equations with the acceleration equations from earlier.

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Problems

• 1. The time the Demon Drop ride is freely falling is 1.5 s. A) What is its velocity at the end of this time? B) How far does it fall?

• A brick falls freely from a high scaffold. A) What is its velocity after 4.0 s? B) How far does the brick fall during the first 4.0 s?

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• What is the velocity of an object at its highest point?

• What is the velocity of an object when it comes back down.

• What is the acceleration of an object at its highest point?

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Falling objects video