Motion graphspg.11

• Create and interpret graphs of position versus time.

• Calculate velocity from the slope of the position vs. time graph.

• Create and interpret graphs of velocity versus time.

Objectives Physics terms• slope

• average velocity

• instantaneous velocity

Equations

In order to understand motion, you first need be able to describe it.

One way to do this is with graphs.

The simplest motion graph shows the position of an object at each moment of time.

Graphing motion

• Position (+/-) is on the vertical (y) axis• Time is on the horizontal (x) axis

Position vs. timePosition vs. time graphs show how the position of an object changes over time.

Each point on the graph represents an object being at a particular place at a particular time.

Position vs. time graph practiceHow would you represent an object at a position of10 meters at 8 seconds?

How would you represent an object at a position of -2m at 2 seconds?

Creating a position vs. time graph• Follow the steps given below to draw the correct

position vs. time graph using the graph on the next slide:

• You start at 0 meters at t = 0 seconds

• Then you move to a position of 12 meters at 4 seconds

• Now you’re tired so you stop for one second

• Next you move back to 0m in the next 4 seconds.

Creating a position vs. time graph

P vs. t graph & velocity• For line 1 on your graph (from 0s-4s):

– Object is: Changing position ORStaying still

– Position change is: Constant OR Not constant OR Zero

– Speed is: Constant OR Not constant– Velocity is: Positive OR Negative OR

Zero– Slope is: Positive OR Negative

OR Zero

• For line 2 on your graph (from 4s-5s):– Object is: Changing position OR

Staying still– Position change is: Constant OR Not constant OR

Zero– Speed is: Constant OR Not constant– Velocity is: Positive OR Negative OR

Zero– Slope is: Positive OR Negative

OR Zero

P vs. t graph & velocity• For line 3 on your graph (from 5s-9s):

– Object is: Changing position ORStaying still

– Position change is: Constant OR Not constant OR Zero

– Speed is: Constant OR Not constant– Velocity is: Positive OR Negative OR

Zero– Slope is: Positive OR Negative

OR Zero

• Velocity (+/-) is on the vertical (y) axis

• Time is on the horizontal (x) axis

Velocity vs. timeVelocity vs. time graphs show how an object’s velocity changes over time.

Velocity vs. time graph practice• How would you represent an

object moving with a constant velocity of 4m/s for 8 seconds?

• How would you represent an object moving with a constant velocity of -2m/s for 4s & then changing its speed by 2m/s every second for 4s?

Creating a velocity vs. time graph• Follow the steps given below to draw the correct

velocity vs. time graph using the graph on the next slide:

• An object moves forward at 5m/s for 5 seconds

• Then it turns around & moves backward at 5m/s for 5 more seconds

Creating a velocity vs. time graph

Importance of SlopeFinding slope can help us describe how an object’s motion is changing.

Taking the slope of a line on a position vs. time graph tells you the objects velocity.

Taking the slope of a line on a velocity vs. time graph tells you the objects acceleration.

SlopeTo find slope of a line pick 2 points on the line & plug them into the slope formula

Using slope• Below on the left is a p vs. t graph. Draw the V vs. t

graph that corresponds to the p vs. t graph.

3 m/s

Put the graphs together

An object moves from 0 meters to 12 meters in 4 seconds.

Next, it stands still for 1 second, then moves back again in 4 more seconds.

3 m/s

What does the velocity graph look like?

Put the graphs together

An object moves from 0 meters to 12 meters in 4 seconds.

Next, it stands still for 1 second, then moves back again in 4 more seconds.

3 m/s

-3 m/s

Put the graphs together

An object moves from 0 meters to 12 meters in 4 seconds.

Next, it stands still for 1 second, then moves back again in 4 more seconds.

In most situations the velocity is not constant.

The instantaneous velocity is the velocity at a given instant.

Can you find this object’s instantaneous velocity at:

• 4 seconds?

• 8 seconds?

• 13 seconds?

Instantaneous velocity

End at 70 m

Start at 15 m

Start at 3 s End at 14 s

Average velocity The average velocity is the total change in position divided by the total change in time.

What is the object’s average velocity?

𝑉 𝑎𝑣𝑔=∆ 𝑥∆𝑡

=𝑥 𝑓 −𝑥 𝑖

𝑡 𝑓 −𝑡 𝑖

1. Where is the speed zero?

2. Where do the two graphs NOT match?

3. Where is the motion forward and where is it backward?

4. Between 1 and 2 seconds, how much distance is covered?

At (B), where the slope is zero.

Homework

At (C); the position graph has a slope of 2 m/s, but the velocity graph shows 4 m/s.

(A) and (C) are forward, (D) is backward.

6 meters

4. Sketch these graphs if the velocity at (A) and (C) were changed to 3 m/s.

Homework