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Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion. Dynamics deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as Mechanics. 2.1 Displacement. 2.1 Displacement.

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slide2

Kinematics deals with the concepts that

are needed to describe motion.

Dynamics deals with the effect that forces

have on motion.

Together, kinematics and dynamics form

the branch of physics known as Mechanics.

2 2 speed and velocity
2.2 Speed and Velocity

Average speed is the distance traveled divided by the time

required to cover the distance.

SI units for speed: meters per second (m/s)

2 2 speed and velocity1
2.2 Speed and Velocity

Example 1 Distance Run by a Jogger

How far does a jogger run in 1.5 hours (5400 s) if his

average speed is 2.22 m/s?

2 2 speed and velocity2
2.2 Speed and Velocity

Average velocity is the displacement divided by the elapsed

time.

2 2 speed and velocity3
2.2 Speed and Velocity

Example 2 The World’s Fastest Jet-Engine Car

Andy Green in the car ThrustSSC set a world record of

341.1 m/s in 1997. To establish such a record, the driver

makes two runs through the course, one in each direction,

to nullify wind effects. From the data, determine the average

velocity for each run.

2 3 acceleration
2.3 Acceleration

The notion of acceleration emerges when a change in

velocity is combined with the time during which the

change occurs.

2 3 acceleration1
2.3 Acceleration

DEFINITION OF AVERAGE ACCELERATION

2 3 acceleration2
2.3 Acceleration

Example 3 Acceleration and Increasing Velocity

Determine the average acceleration of the plane.

2 3 acceleration4
2.3 Acceleration

Example 3 Acceleration and Decreasing

Velocity

2 4 equations of kinematics for constant acceleration
2.4 Equations of Kinematics for Constant Acceleration

Equations of Kinematics for Constant Acceleration

2 4 equations of kinematics for constant acceleration1
2.4 Equations of Kinematics for Constant Acceleration

Five kinematic variables:

1. displacement, x

2. acceleration (constant), a

3. final velocity (at time t), v

4. initial velocity, vo

5. elapsed time, t

2 4 equations of kinematics for constant acceleration3
2.4 Equations of Kinematics for Constant Acceleration

Example 6 Catapulting a Jet

Find its displacement.

2 5 applications of the equations of kinematics
2.5 Applications of the Equations of Kinematics

Reasoning Strategy

1. Make a drawing.

2. Decide which directions are to be called positive (+) and

negative (-).

3. Write down the values that are given for any of the five

kinematic variables.

4. Verify that the information contains values for at least three

of the five kinematic variables. Select the appropriate equation.

5. When the motion is divided into segments, remember that

the final velocity of one segment is the initial velocity for the next.

6. Keep in mind that there may be two possible answers to a

kinematics problem.

2 5 applications of the equations of kinematics1
2.5 Applications of the Equations of Kinematics

Example 8 An Accelerating Spacecraft

A spacecraft is traveling with a velocity of +3250 m/s. Suddenly

the retrorockets are fired, and the spacecraft begins to slow down

with an acceleration whose magnitude is 10.0 m/s2. What is

the velocity of the spacecraft when the displacement of the craft

is +215 km, relative to the point where the retrorockets began

firing?

2 6 freely falling bodies
2.6 Freely Falling Bodies

In the absence of air resistance, it is found that all bodies

at the same location above the Earth fall vertically with

the same acceleration.

This idealized motion is called free-falland the acceleration

of a freely falling body is called the acceleration due to

gravity.

2 6 freely falling bodies2
2.6 Freely Falling Bodies

Example 10 A Falling Stone

A stone is dropped from the top of a tall building. After 3.00s

of free fall, what is the displacement y of the stone?

2 6 freely falling bodies5
2.6 Freely Falling Bodies

Example 12 How High Does it Go?

The referee tosses the coin up

with an initial speed of 5.00m/s.

In the absence if air resistance,

how high does the coin go above

its point of release?

2 6 freely falling bodies8
2.6 Freely Falling Bodies

Conceptual Example 14 Acceleration Versus Velocity

There are three parts to the motion of the coin. On the way

up, the coin has a vector velocity that is directed upward and

has decreasing magnitude. At the top of its path, the coin

momentarily has zero velocity. On the way down, the coin

has downward-pointing velocity with an increasing magnitude.

In the absence of air resistance, does the acceleration of the

coin, like the velocity, change from one part to another?

2 6 freely falling bodies9
2.6 Freely Falling Bodies

Conceptual Example 15 Taking Advantage of Symmetry

Does the pellet in part b strike the ground beneath the cliff

with a smaller, greater, or the same speed as the pellet

in part a?

position time graphs
We can use a postion-time graph to illustrate the motion of an object.

Postion is on the y-axis

Time is on the x-axis

Position-Time Graphs
plotting a distance time graph
Axis

Distance (position) on y-axis (vertical)

Time on x-axis (horizontal)

Slope is the velocity

Steeper slope = faster

No slope (horizontal line) = staying still

Plotting a Distance-Time Graph
where and when
We can use a position time graph to tell us where an object is at any moment in time.

Where was the car at 4 s?

30 m

How long did it take the car to travel 20 m?

3.2 s

Where and When
describing in words1
Describe the motion of the object.

When is the object moving in the positive direction?

Negative direction.

When is the object stopped?

When is the object moving the fastest?

The slowest?

Describing in Words
accelerated motion
Accelerated Motion
  • In a position/displacement time graph a straight line denotes constant velocity.
  • In a position/displacement time graph a curved line denotes changing velocity (acceleration).
  • The instantaneous velocity is a line tangent to the curve.
accelerated motion1
Accelerated Motion
  • In a velocity time graph a line with no slope means constant velocity and no acceleration.
  • In a velocity time graph a sloping line means a changing velocity and the object is accelerating.
velocity
Velocity
  • Velocity changes when an object…
    • Speeds Up
    • Slows Down
    • Change direction
velocity time graphs
Velocity is placed on the vertical or y-axis.

Time is place on the horizontal or x-axis.

We can interpret the motion of an object using a velocity-time graph.

Velocity-Time Graphs
constant velocity
Objects with a constant velocity have no acceleration

This is graphed as a flat line on a velocity time graph.

Constant Velocity
changing velocity
Objects with a changing velocity are undergoing acceleration.

Acceleration is represented on a velocity time graph as a sloped line.

Changing Velocity
positive and negative velocity
The first set of graphs show an object traveling in a positive direction.

The second set of graphs show an object traveling in a negative direction.

Positive and Negative Velocity
speeding up and slowing down
Speeding Up and Slowing Down
  • The graphs on the left represent an object speeding up.
  • The graphs on the right represent an object that is slowing down.
two stage rocket
Two Stage Rocket
  • Between which time does the rocket have the greatest acceleration?
  • At which point does the velocity of the rocket change.
displacement from a velocity time graph
The shaded region under a velocity time graph represents the displacement of the object.

The method used to find the area under a line on a velocity-time graph depends on whether the section bounded by the line and the axes is a rectangle, a triangle

Displacement from a Velocity-Time Graph