Motion

Unit 1: MotionChapter 2: Describing Motion

2.1 Position, Velocity, and Acceleration

2.2 Position vs. Time Graphs

2.3 Velocity vs. Time Graphs

2.1 Investigation: Position, Speed, and Velocity

Key Question:

How are position, speed, and velocity related?

Objectives:

Measure positive and negative positions.

Measure positive and negative velocity.

Compare speed and velocity.

Position, Velocity, and AccelerationPosition is a variable.

Position and distance are similar but not the same. Both use units of length.

Position is given relative to an origin.

If a car moves 20 cm, what is it’s new

position?

Position and displacement A change in position is called displacement.

A displacement of –20 cm means the car leaves the 50-cm mark and moves toward the origin.

A displacement of 20 cm means the car moves away from the origin.

VelocityThe velocity of an object (v) tells

you both its speed and its direction of motion.

Velocity can be positive or negative, so it includes information about the moving object’s direction.

Constant velocity means that both the speed and the direction an object is traveling remains constant.

Positive velocity

The sign for velocity is based on the calculation of a change in position.

The change in position is the final position minus the initial position.

Negative velocity

Negative velocity means the position is decreasing relative to the starting point.

Velocity

Average and instantaneous velocityAverage velocity is the total displacement divided

by the total time taken.

Instantaneous velocity describes the velocity of an object at one specific moment in time or at one specific point in its path.

Relative velocityRelative velocity

describes the velocity of an object with respect to a frame of reference.

If you are sitting in a chair, you are not moving relative to Earth, but you are moving at about 67,000 mph relative to the Sun.

A people mover has a velocity of 1 m/s and is 150 m long. If a man walks 2 m/s relative to the people mover, how long will it take him to reach the opposite end if he walks in the direction that the people mover travels?

Using relative velocity

1. Looking for: …the time in seconds.

2. Given: … velocity of the people mover (1 m/s), the relative velocity of the walker (2 m/s), and the displacement (150 m).

3. Relationship: Use this version of the velocity equation:

t = Δx ÷ v

4. Solution: t = 150 m ÷ (1 m/s + 2 m/s)

= 150 m ÷ 3 m/s = 50 s

Acceleration

Acceleration is the rate at which velocity changes.

AccelerationAcceleration and velocity are completely different

ways to describe an object’s motion.

An object can be accelerating when its velocity is zero.

Like velocity, acceleration can be positive or negative.

An object will have a positive acceleration when it is speeding up in the positive direction, and when it is slowing down in a negative direction.

Calculating acceleration

A sailboat moves at 1 m/s. Wind increases its velocity to 4 m/s in 3 seconds. Calculate the acceleration.

Calculating acceleration

1. Looking for: .. the acceleration in m/s/s.

2. Given: … the initial velocity (vi=1 m/s), final velocity (vf=4 m/s), and time (t=3 s)

3. Relationship: Use: a = (vf – vi) ÷ t

4. Solution: a = 4 m/s – 1 m/s = 3 m/s = 1 m/s

3 s 3 s

Units of accelerationAn acceleration in “meters per second per second

(m/s/s) is often written m/s2 or meters per second squared.

Unit 1: MotionChapter 2: Describing Motion

2.1 Position, Velocity, and Acceleration

2.2 Position vs. Time Graphs

2.3 Velocity vs. Time Graphs

2.2 Investigation: Position, Velocity, and Time GraphsKey Question:

How are graphs used to describe motion?

Objectives:

Create graphs of velocity versus position and time.

Create a predictive model for the velocity of car rolling down a hill.

Position vs. Time Graphs Motion graphs are an important

tool used to show the relationships between position, velocity, acceleration, and time.

Graphs help test drivers and engineers see how much of the straight track each car covered in equal time intervals.

Drivers can make adjustments in how they operate cars.

SlopeThe slope of a line is the

ratio of the “rise,” or vertical change, to the “run,” or horizontal change.

The rise is equal to the height of the triangle.

The run is equal to the length along the base of the triangle.

Position vs. Time Graphs

A position vs. time graph can tell you whether an object’s velocity is constant or changing. (Both cars have constant velocity, but Car A is faster than Car B.)

If the velocity is constant, the graph is a straight line with a constant slope.

Position vs. time graphs of accelerated motion

If the velocity is changing, the slope changes, so the graph curves.

Position vs. time graphs of accelerated motion

The graph of an object slowing down is also curved.

An example is a car coming to a gradual stop at a red light.

Unit 1: MotionChapter 2: Describing Motion

2.1 Position, Velocity, and Acceleration

2.2 Position vs. Time Graphs

2.3 Velocity vs. Time Graphs

2.3 Investigation: Position, Velocity, and Time GraphsKey Question:

What happens to the velocity of an object as it moves downhill?

Objectives: Explain the motion of the Energy Car, in terms of velocity and

acceleration, as it moves along an inclined track. Infer the meaning of acceleration from a velocity versus time

graph. Apply the acceleration formula to solve problems.

Velocity vs. time graphs

The velocity vs. time graph has velocity on the y-axis and time on the x-axis.

On this graph, constant velocity is shown with a straight horizontal line.

Velocity vs. time graphs

The velocity vs. time graph is the best tool for understanding acceleration.

It clearly shows how the velocity of an object changes with time.

Constant acceleration

The velocity vs. time graph shown is for a ball in free fall.

Since the ball is accelerated by gravity, it’s velocity increases by the same amount: 9.8 m/s2.

What is the velocity of the ball after 4 seconds?Ans: 29.4 + 9.8 = 39.2 m/s2 ,down

Constant acceleration

Don’t confuse constant velocity with constant acceleration.

Constant velocity means an object’s position changes by the same amount each second.

Constant acceleration means an object’s velocity changes by the same amount each second.

Calculating acceleration

The slope of a velocity vs. time graph represents the acceleration of the object.

Calculating acceleration

The slope of a graph is equal to the ratio of rise to run.

The rise is the amount the velocity changes.

The run is the amount the time changes.

Calculate the acceleration shown on the graph.

Calculating acceleration from a graph

1. Looking for: … the acceleration in m/s/s.2. Given: … a graph of velocity vs. time3. Relationship: The acceleration is equal to the

slope of the line. 4. Solution: slope = rise = 40 m/s = 4 m/s2

run 10 s

DisplacementThe velocity vs. time graph gives us a way to

calculate the object’s displacement even when its velocity is changing.

The displacement is equal to the area on the graph.

DirectionTo show direction on a velocity vs. time graph, we

must include a portion of the graph that shows negative velocities.

Motion Graph Summary

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