Upload
michaeldelaney8541
View
602
Download
0
Embed Size (px)
Citation preview
DISTANCE TIME GRAPHS
� Distance is always represented on the y axis (vertical) of the graph.
It must always be accompanied by a distance unit (short
form) in brackets. Example: (m) for meters.
� Time is always represented on the x axis (horizontal) of the graph.
It must always be followed by a time unit in brackets. (s)
� The steeper the slope of the graph, the greater the speed. � The slope represents the speed. � In co-ordinate geometry the slope is represented by the
equation y = mx + b
where: y is the dependent variable on the y axis
x is the dependent variable on the x axis
m is the slope of the line
b is the y intercept of the line
� On a distance-time graph, the slope is the speed and so is
represented by the equation
vav = ∆ d
∆ t
where: ∆∆∆∆ d is the distance traveled (dependent variable)
∆∆∆∆ t is the time (independent variable)
vav is the slope of the line (speed)
0 is the y intercept ( initial distance or d1 )
From a graph, the speed of an object can be determined by finding
the slope of the line with the following equation:
slope = rise
run
= ∆d
∆t
= d2 - d1
t2 - t1
= ____ m/s or km/h
The speed is determined using the slope of the best-fit straight line of the distance time-graph.
Sample Problem
What is the speed of Hank’s bike over 100 m?
Several of Hank’s friends are positioned 20.0 m apart with
stopwatches. All the friends start their stopwatches when Hank
starts to pedal his bike in a straight line. Each friend stops her
watch when Hank reaches her position.
Evidence
Hank’s Bike Ride
Distance (m) Time (s)
0.0 0.0
20.0 6.0
40.0 9.0
60.0 16.0
80.0 19.0
100.0 25.0
(a) Plot a distance-time graph of Hank’s bike ride.
(b) Calculate the slope of the best-fit line and answer the Question.
(c) Evaluate the design. What alternative design would be more
efficient?