9.7 Distance-time Graph Notes
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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) 0.0 20.0 40.0 60.0 80.0 100.0
Time (s) 0.0 6.0 9.0 16.0 19.0 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?
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) 0.0 20.0 40.0 60.0 80.0 100.0
Time (s) 0.0 6.0 9.0 16.0 19.0 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?
