• Putting it all togetherPutting it all together• Combining d-t and v-t graphsCombining d-t and v-t graphs• Problem solving with d-t and v-t graphsProblem solving with d-t and v-t graphs

• A common mistake by Physics 20 students is when they assume that A common mistake by Physics 20 students is when they assume that different types of graphs work the exact same way. different types of graphs work the exact same way.

• The graphs can be related to each other, but that doesn’t mean you The graphs can be related to each other, but that doesn’t mean you look at them the same way. look at them the same way.

1) An object moves at a 1) An object moves at a

constant velocity.constant velocity.

d vs td vs t v vs tv vs t

2) An object stops moving.2) An object stops moving.

3) An object speeds up at a 3) An object speeds up at a constant rate.constant rate.

d vs td vs t v vs tv vs t

4) An object slows down at a 4) An object slows down at a constant rate.constant rate.

d vs td vs t v vs tv vs t

Graphing SummaryDISTANCE – TIME

graphsVELOCITY – TIME

graphsSlope = velocity Slope = accelerationArea under the curve has NO useful meaning

Area under the curve = displacement

• AccelerationAcceleration– Rate of change in velocity or speedRate of change in velocity or speed– Found using SLOPE of a v-t graphFound using SLOPE of a v-t graph– Units m/sUnits m/s22

• DisplacementDisplacement– Can be found as the area under the graph Can be found as the area under the graph – May need to be split up (triangle / square / May need to be split up (triangle / square /

rectangle)rectangle)

Bart starts from Airdrie and drives north at 80 Bart starts from Airdrie and drives north at 80 km/h. Lisa starts 30 minutes after Bart and km/h. Lisa starts 30 minutes after Bart and drives at 120 km/h north. At what time and drives at 120 km/h north. At what time and position will Lisa pass Bart?position will Lisa pass Bart?

You can solve byYou can solve by– Creating a data tableCreating a data table– Constructing a graphConstructing a graph– Constructing a system of equationsConstructing a system of equations

Given the velocity vs. time graph belowGiven the velocity vs. time graph belowa.a. What is the average acceleration?What is the average acceleration?b.b.What is the change in displacement? (+ or -)What is the change in displacement? (+ or -)

9.09.0

24.024.0

0.00.0

Velo

city

Ve

loci

ty

(m/s

)(m

/s)

Time (s)Time (s)

• Find the acceleration at 6.0 sFind the acceleration at 6.0 s• What is the total displacement after 10.0 sWhat is the total displacement after 10.0 s

10.010.0

4.04.0

0.00.0

Velo

city

Ve

loci

ty

(m/s

)(m

/s)

Time (s)Time (s)

12.012.0

6.06.0

• What is the total displacement?What is the total displacement?• Sketch a corresponding d-t graph.Sketch a corresponding d-t graph.• What is the average velocity from 0 – 18 s?What is the average velocity from 0 – 18 s?

00

Velo

city

Ve

loci

ty

(m/s

)(m

/s)

8.08.0

0.00.0Time (s)Time (s)

-4.0-4.0

1010 1818

• Draw the Draw the corresponding v – t corresponding v – t graph for the d – t graph for the d – t graph given.graph given.

Graph of Distance versus Time

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25

Time (s)

Dis

tan

ce (

m)

• Need to know SPEED if we need to draw a Need to know SPEED if we need to draw a speed-time graphspeed-time graph

• Speed from d-t graph = SLOPESpeed from d-t graph = SLOPE

Graph of Distance versus Time

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25

Time (s)

Dis

tan

ce (

m)

Using (0,0) and (25,75) as our Using (0,0) and (25,75) as our two points.two points. RiseRise == 75 m – 0 m75 m – 0 mRunRun 25 s - 0 s 25 s - 0 s

= 3 m/s= 3 m/s

• Diagonal line on a d-t graph means CONSTANT Diagonal line on a d-t graph means CONSTANT MOTION so the object is STAYING at 3 m/sMOTION so the object is STAYING at 3 m/s

• Draw the corresponding v-t graphDraw the corresponding v-t graphGraph of Speed versus Time

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25

Time (s)

Sp

eed

(m

/s)