Graphs of motion Contents:• Position graphs

• Whiteboard• Qualitative• Instantaneous

• Velocity graphs• Whiteboard• Qualitative

Position vs. Time graphs

TOC

Pos

itio

n in

met

ers

Time in seconds 5 s

4 m

(still at 2, 2 in 5, 4 in 2, -4 in 4)

Slope = rise/runSlope = Velocity

Whiteboards: Position vs. time

1 | 2 | 3 | 4

TOC

W

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What is the velocity at 2.0 seconds?

.67 m/s

W

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What is the velocity at 4.0 seconds?

0

W

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What is the velocity at 6.2 seconds?

2.0 m/s

W

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What is the velocity at 8.15 seconds?

-3.0 m/s

Whiteboards: Qualitative Position vs. time

TOC

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s going on here?

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

v at 6.0 s =? Find the tangent slope

Finding instantaneous velocity

5.1/5.95.86 ms

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What is the velocity at 3.0 seconds?

3/7.6 = .39 m/s

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s the velocity at 6.0 seconds?

-2.85/4.5 = -.62 m/s

Pos

itio

n in

met

ers

Time in seconds 5 s

5 m

What’s the velocity at 6.0 seconds?

5.65/6.9 = .82 m/s

Velocity vs. Time graphs

TOC

Vel

ocit

y (m

/s)

Time in seconds 5 s

4 m/s

Slope = rise/runSlope = acceleration

(show driving on a road)

Area under is Displacement

3 m/s for 5 secondsHow far?

LxW = ?

Velocity vs. Time graphs

TOC

Vel

ocit

y (m

/s)

Time in seconds 5 s

4 m/s

Slope = rise/runSlope = acceleration

(show driving on a road)

Area under is Displacement

Now how far?

Whiteboards: Velocity vs. time

1 | 2 | 3 | 4

TOC

velo

city

in m

/s

Time in seconds 5 s

5 m/s

What is the acceleration at 1.15887 seconds?

1.5 m/s/s

velo

city

in m

/s

Time in seconds 5 s

5 m/s

What is the acceleration at 8.1 seconds?

-.5 m/s/s

velo

city

in m

/s

Time in seconds 5 s

5 m/s

What displacement between 2 and 4 seconds?

6.0 m

velo

city

in m

/s

Time in seconds 5 s

5 m/s

What displacement between 4 and 7 seconds?

13.5 m

Whiteboards: Qualitative Velocity vs. time

TOC

Time

+ V

What’s going on here?

0 m/s

- V

Time

+ V

What’s going on here?

0 m/s

- V

Time

+ V

What’s going on here?

0 m/s

- V

Time

+ V

What’s going on here?

0 m/s

- V

Time

+ V

What’s going on here?

0 m/s

- V

Time

+ V

What’s going on here?

0 m/s

- V

Pos

itio

n

Time

Here is what it is as position v time