Position vs. TimePosition vs. Time

Analysis of a Position vs. Time Analysis of a Position vs. Time GraphGraph

Determining the motion on a Determining the motion on a D vs. T GraphD vs. T Graph

Where did the object start?Where did the object start?

Which direction did it go?Which direction did it go?

Where did the object stop?Where did the object stop?

Is the motion uniform (constant)?Is the motion uniform (constant)?

Is the motion non-uniform (changing)?Is the motion non-uniform (changing)?

Can you tell which is faster? (if 2 or Can you tell which is faster? (if 2 or more objects are present)more objects are present)

Position vs. Time Graphs & Position vs. Time Graphs & VelocityVelocity

We can calculate velocity using We can calculate velocity using Position vs. Time GraphsPosition vs. Time Graphs

Velocity is a vector quantity because Velocity is a vector quantity because it has both magnitude & direction.it has both magnitude & direction.– It tells us not only the speed that an It tells us not only the speed that an

object is traveling, but also its directionobject is traveling, but also its direction

Distance RiseDistance Rise

Velocity = ----------- = -------Velocity = ----------- = -------

Time RunTime Run

Using slope to predict motionUsing slope to predict motionOn a On a distance vs. timedistance vs. time graph graph– If slope is 0, then velocity is 0.If slope is 0, then velocity is 0.– If slope is positive, velocity is If slope is positive, velocity is

constant in positive direction.constant in positive direction.– If slope is negative, velocity is If slope is negative, velocity is

constant in the opposite direction.constant in the opposite direction.– If slope is changing, velocity is If slope is changing, velocity is

changing.(i.e. you are changing.(i.e. you are accelerating)accelerating)

d(m)

t(s)

A

Object A is stationary at some positive position from the origin.

d(m)

t(s)

B

Object B moves Object B moves away from origin away from origin with a constant with a constant positive velocity.positive velocity.

d(m)

t(s)

C

Object C start at some positive position and moves away from the origin at a constant positive velocity.

d(m)

t(s)

D

Object D moves away from the origin at a constant positive velocity (slower than previous examples).

d(m)

t(s)

E

Object E start at some positive position and walks toward the origin with a constant velocity.

Distance vs. Time Graphs with Non-Uniform Motion

Changing velocity

(speeding up)

Changing velocity

(slowing down)

ExampleExample

d(m)

t(s)

A

B

D

C

Slower than B or C.

Same velocity as

B. V=0

Constant +V

PRACTICEPRACTICE

Practice #1

• Imagine you are riding your bike down Detroit Rd.

• Compare the lines A-D– Think of magnitude & direction!

Nagel Rd. (East)

Route 83/ Center Rd.

Stoney Ridge (West)

A

B

D

C

Practice #2• Determine the Time & Distances for the graph below

Time (s)

Position (m)

0

2.5

5

7.5

10

12.5

Practice #3• Calculate the velocities for the following:

East

Practice #4• Match the story to the graph below