Distance-Time Graphs

Applied Physics 11

Distance-Time Graphs Distance-time graphs are a way to visually

show a collection of data. They allow us to get a visual understanding of

speed. X-axis time Y-axis distance

Time (s) Distance (m)

0 0

1 13

2 25

3 40

4 51

5 66

6 78

Slope The proper equation

for a line is y=mx + b

The y is the dependant variable (on y -axis)The x is the independent variable (on x-axis)The m is the slope of the lineThe b is the y intercept of the line.

Slope in a distance-time graph In a distance-time graph the equation

changes from y= mx + b d = vt

d is the dependant variable, lying on the y axis.

t (time) is the independant variable and lies on the x axis.

v (speed) is the slope of the line. 0 (the initial distance) is the y intercept.

Slope and Speed In a distance time-graph, the slope

determines the speed. The steeper the slope, the greater the speed.

The object shown in graph A is travelling at a greater speed. It is covering a greater distance in a shorter time.

Finding speed from slope Slope (or v) is

equal to: y/Δx Δd/Δt Change in

distance/change in time

RISE over RUN

Rise over Run

Δd = d2 –d1

Δd = 7.7km - 1.9km Δd = 5.8km Δt = t2 – t1

Δt = 11.2min - 2.7min Δt = 8.5min v = Δd/Δt v = 5.8/8.5 v=0.68km/min

p 364

Time (min)

Distance (km)

0 0

1 1.0

2 1.8

3 2.9

4 4.2

5 5.0

6 5.9

7 6.9

8 8.2

9 9.2

10 10.0

Time (min)

Dis

tance

(m

)

0 1 2 3 4 5 6 7 8 9 10

9 8 7 6 5 4 3 2 1 0

Time (min)

Distance (km)

0 0.0

2.0 2.4

4.0 4.8

6.0 7.2

8.0 9.6

10.0 12.0

12.0 14.4

0 1 2 3 4 5 6 7 8 9 10 11 12 13

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Time (s)

Dis

tance

(km

)