2.1 Displacement & Velocity

Biblical Reference

Both were running, but the other disciple outran Peter and reached the tomb first.

John 20:4

Physics is the study of the physical world, and the movement of objects is big part of the physical world.

Start with 1 dimensional motion. (straight line)

Representing Motion

1) Describe motion in terms of motion diagrams.

2) Develop a particle model to represent a moving object.

3) Describe motion in terms of frame of reference, displacement, time, speed, and velocity.

4) Calculate the displacement of an object traveling at known velocity for a specific time interval.

Physics is the study of the physical world, and the movement of objects is big part of the physical world.

Start with 1 dimensional motion. (straight line)

Representing Motion

5) Construct and interpret position vs. time graphs.

6) Recognize the difference between scalar and vector.

7) Distinguish the difference between instantaneous velocity and average velocity.

8) Use motion equations to interpret graphs and solve motion problems.

How do you know if an object is moving?

• It depends completely on how you want to look at the moving object. You establish a frame of reference.

• A frame of reference allows you to measure the changes in position of an object.

Example: You are sitting in an airplane which is moving at a speed of 100 km/h and there is a fly sitting on your head.

(a) What is your speed relative to the ground?

(b) What is your speed relative to the seat you're sitting in?

(c) What is the speed of the fly relative to you?

Motion is RELATIVE

A Motion Diagram shows the position of an object at equal time intervals.

Motion Diagram

A Particle Model shows the position of an object in equal time intervals - the object is represented as a dot/particle

Particle Model

Here is the particle model of two toy cars. At any time in there motion, are they going the same speed?

Particle Model

Coordinate Systems – provide more data about the motion diagram. (origin, direction, position, distance from the origin, displacement)

Coordinate System

The ball is moving in the positive x-direction.

Scalar – a value without direction (Time, Mass, Distance)

Vector – a value with direction.

Resultant – The sum of two or more vectors.

Scalar vs. Vector

4 m East

Displacement – Change in Position Not necessarily the total distance traveled.

– Displacement is relative to an axis.– Distance is how far you have traveled regardless

of direction.

"x" displacement - moving horizontally either right or left.

"y" displacement - moving vertically either up or down.

Change is expressed using the Greek letter DELTA ( Δ ).

Δx = xf - xi or Δy = yf - yi

ExampleSuppose a person moves in a straight line from the lockers (at a position  x = 1.0 m) toward the physics lab (at a position x = 9.0 m).

The answer is positive. So the person must have been traveling horizontally to the right.

ExampleSuppose the person turns around!

The answer is negative so the person must have been traveling horizontally to the left

What is the DISPLACEMENT for the entire trip?

What is the total DISTANCE for the entire trip?

mxxx initialfinal 00.10.1

m1688

Displacement

The displacement of a particle is defined as its change in position.

Note: Displacement to the right is positive

mx

mmx

xxx

2

460

0 2 4 6-2-4-6

x

(m)

0 2 4 6-2-4-6

x

(m)

Displacement

The displacement of a particle is defined as its change in position.

Note: Displacement to the left is negative

mx

mmx

xxx

12

660

0 2 4 6-2-4-6

x

(m)

Displacement

The displacement of a particle is defined as its change in position.

mx

mmx

xxx

8

)6(20

Note: Displacement to the right is positive

A student walks 70 m East, then walks 30 m West.What is the magnitude of the students net displacement?

A) 30 m

B) 40 m

C) 70 m

D) 100 m

m 40m 03m 70 21

xxxnet

EastWest

70 m

30 m

Displacement

East

40 m

Displacement

Position vs. Time Graphs• Plots a moving objects position compared

to its time.

Position vs Time

16 2412840 20 28

(s)

x

4

8

12

16

20

24

28

(m)

1 2 3 4t

5

An object starts from rest and moves with constant acceleration.

Motion Graphs

Position vs. Time Graphs

Average VelocityVelocity (vector): The rate at which displacement changes.

Rate = Any quantity divided by time.

Speed (scalar): The rate at which distance changes.

t

ds

ExampleA football player runs 300. m in 1.50 min towards the far end of the field and then runs back to his starting point in 1.80 min. What was the player’s average velocity (a) in running to the far end of the field (b) coming back to the starting point, and (c ) for the total run.

s

mmm

t

xxv ifavg 33.3

sec90

0300

s

mmm

t

xxv ifavg 78.2

sec108

3000

s

mmm

t

xxv ifavg 00.0

sec198

00

Slope – A basic graph model

Look at the formula for velocity.

What is the slope?

What is the y-axis or the rise?

What is the x-axis or the run? 

For a Displacement vs. Time graph, the velocity of an object during a specific time intervals is the slope.

t

xv

Run

Riseslope

Velocity

Displacement

Time

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals

(a) 0 to 2 s

(b) 0 to 4 s

(c) 2 s to 4 s

(d) 4 s to 7 s

(e) 0 to 8 s.

x

t

tx

v

sm 0.5

02010

v

Motion Graphs

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals

(a) 0 to 2 s

(b) 0 to 4 s

(c) 2 s to 4 s

(d) 4 s to 7 s

(e) 0 to 8 s.

x

t

tx

v

sm 25.1

0405

v

Motion Graphs

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals

(a) 0 to 2 s

(b) 0 to 4 s

(c) 2 s to 4 s

(d) 4 s to 7 s

(e) 0 to 8 s.

x

t

tx

v

sm 5.2

24105

v

Motion Graphs

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals

(a) 0 to 2 s

(b) 0 to 4 s

(c) 2 s to 4 s

(d) 4 s to 7 s

(e) 0 to 8 s.x

t

tx

v

sm 33.3

4755

v

Motion Graphs

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals

(a) 0 to 2 s

(b) 0 to 4 s

(c) 2 s to 4 s

(d) 4 s to 7 s

(e) 0 to 8 s.t

tx

v

sm 0.0

0800

v

Motion Graphs

(s)

x

48

1216202428

(m)

1 2 3 4 t5

Slope Acceleration Graph

Average Velocity Motion Equation #1

di = -2 m

Average velocity = 5.5 m/s

y = mx + b

y = (5.5m/s)x + -2m

Equation of motion for average velocity

d = vt + di

ExampleA bicyclist travels at a constant speed of 4.0 m/s for 5.0s. How far does he go?

mmss

mdvtd i .200.0)0.5)(0.4(

• Determine whether each set of data shows constant velocity or acceleration.

Calculator Exercise

Time (s) Distance (m)

0 5

1 7.1

2 12.8

3 23.2

4 36.9

Time (s) Distance (m)

0 5

1 7.1

2 8.9

3 11.2

4 13.1