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Chapter 2 - Motion in One Dimension

- 2.1 - Displacement and Velocity

Motion

- One-dimensional motion is the simplest form of

motion - e.g. a train on a straight track (forward or

backward) - In this chapter we will consider only

one-dimensional motion

Motion

- The first step in analyzing motion is to choose a

frame of reference. - If an object is at rest, its position does not

change with respect to a frame of reference. - When we choose this frame of reference, we need

to remember to remain consistent.

Displacement

- Displacement is the change in position of an

object. - It is the length of the straight line drawn from

its initial position to its final position

Displacement change in position final

position - initial position

Displacement

- Displacement is not always equal to the distance

traveled

Displacement

- Displacement can be positive or negative

Average Velocity

- Knowing the distance traveled or the displacement

doesnt tell completely describe the motion of an

object - Knowing the speed is important for evaluating

motion - Average velocity is the total displacement

divided by the time interval during which the

displacement occurred

Average Velocity

- The Average Velocity can be positive or negative
- Equal to the constant velocity needed to cover

the given displacement in a given time interval - It is NOT the average of the starting and ending

velocities - Example A car travels from city A to city B (100

km). If the first half of the distance is driven

at 50 km/h and the second half is driven at 100

km/h, what is the average velocity of the car?

Practice

- Page 44, Practice 2A

Average Speed

- Velocity is not the same as speed
- Velocity has both magnitude AND direction
- Speed has only a magnitude

Graphical Interpretation of Velocity

- In a position-time graph, we can determine the

vavg by drawing a straight line between two

points on the graph

Graphical Interpretation of Velocity

Instantaneous Velocity

- The velocity of an object at some instant

Chapter 2

- Section 2.2 - Acceleration

Acceleration

- Most objects in motion dont move with a constant

velocity - Acceleration measures the rate of change in

velocity in a given time interval

Problem

- Find the acceleration of an amusement park ride

that falls from rest to a speed of 28m/s in 3.0s. - 9.3 m/s2

Acceleration

- Acceleration has both magnitude and direction
- If an object (i.e. a car) is moving in the

positive direction and is speeding up, the

acceleration is positive - If an object is moving in the positive direction

and is slowing down, the acceleration is negative - If an object (i.e. a car) is moving in the

negative direction and is speeding up, the

acceleration is negative - If an object is moving in the negative direction

and is slowing down, the acceleration is positive

Constant acceleration

- The slope of a velocity-time graph gives the

acceleration - When acceleration is constant, the velocity is

increased by the same amount during each time

interval. - The displacement for each time interval increases

by the same amount

Displacement

- Depends on
- Initial velocity
- Acceleration
- Time

When acceleration is constant, Vavg is the

average of Vi and Vf

Displacement

- When acceleration is constant

Displacement

- The area under the curve in a graph of velocity

versus time equals the displacement during the

time interval

Problem

- A bicyclist accelerates from 5.0 m/s to a

velocity of 16 m/s in 8 s. Assuming uniform

acceleration, what distance does the bicyclist

travel during this time interval? - 84m

Final Velocity

- Depends on
- Initial velocity
- Acceleration
- Time

Constant Acceleration

Displacement with constant uniform acceleration

Final velocity after any displacement

Remember that the square root may be either

positive or negative

Problem

- 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? - -18.0 m/s2

Summary

HW Assignment

- Page 49, Practice 2B, 1 and 4
- Page 53, Practice 2C, 3 and 4
- Page 55, Practice 2D, 2 - 4
- Page 58, Practice 2E, 2, 5, 6

Chapter 2

- Section 2.3 - Falling Objects

Free Fall

- Motion of an object falling with a constant

acceleration - In the absence of air resistance all objects

dropped near the surface of a planet fall with

the same constant acceleration - The symbol for free-fall acceleration is g
- At the surface of the earth, the magnitude of g

is approximately 9.81 m/s2.

Free Fall

- This acceleration is directed downwards
- a -g -9.81 m/s2
- What goes up, must come down
- Fig 2-15, pg 61
- Initial velocity of 10.5 m/s, acceleration is

-9.81 m/s2 - After 1 s, v 0.69 m/s, acceleration is

-9.81m/s2 - After 2 s, v -9.12 m/s (directed downward), a

9.81 m/s2

Free Fall

Free Fall

- FREELY FALLING OBJECTS ALWAYS HAVE THE SAME

DOWNWARD ACCELERATION

Problem

- A ball is thrown straight up into the air at an

initial velocity of 25.0 m/s. Create a table

showing the balls position, velocity, and

acceleration each second for the first 5.00 s of

its motion. - Find the balls time, position, velocity, and

acceleration at the top of its flight

HW Assignment

- Pages 72 - 75 34, 38, 40, 41, 46, 50, 56