# Speed -Time Graphs for Acceleration

SPEED TIME GRAPHS FOR ACCELERATION January 27th, 2011 Lesson 7 Speed Time Graphs for Acceleration Acceleration is a description of the relationship between speed and time. Essentially it is a change in speed over time. The variables in a speed time graph are speed on the y-axis and time on the xaxis, then the slope (y/x) corresponds y/x) corresponds y/x) corresponds y/x) corresponds x) corresponds to the definition of accleration (y/x) corresponds y/x) corresponds v/x) corresponds y/x) corresponds t) . Therefore, the slope of a speed time

graph is equal to acceleration. Example: The speed of a snowboarder is shown over time in the graph below. The acceleration can be calculated by using the slope. Draw a triangle on the line of best fit to calculate Acceleration of a Snowboarder the slope. 14 12 10 Speed (m/s)

8 vv 6 4 2 tt 0 0 1 2 3 4 Total Time (s)

5 6 7 8 Acceleration of a Snowboarder 14 12 Speed (m/s) 10 8 vv 6 4

2 tt 0 0 1 2 3 4 Total Time (s) 5 6 7

8 Speed Time Graphs The type of slope of a speed graph tells us a lot about the type of acceleration Slope positive value Positive acceleration Increasing in speed The steeper the slope the more the object is accelerating. V t V t Speed Time Graphs

Slope Zero Zero Acceleration - Constant speed V t Speed Time Graphs Slope Negative value Negative acceleration Decreasing speed The steeper the slope the more the object is decelerating. V

t Area Under the Line on a Speed Time Graph Uniform Acceleration The area of a speed time graph can be used to claculate the total distance traveled. Distance units can be obtained by multiplying speed (y/x) corresponds m/x) corresponds s) by time (y/x) corresponds s) Example This also corresponds to the distance as calculated from the defining equation for speed:

Speed (m/s) In the example below, a student is in a 250 m bicycle race. They are accelerating at a rate of 2.0 m/x) corresponds s every 10.0 seconds. Acceleration On a Bicycle 12 10 8 6 4 2 0 0 10 20

30 Time (s) 40 50 60 Two variables multiplied together suggest the area of the geometric shape. The area defined by the dotted lines would represent 500m Acceleration On a Bicycle Speed (m/s) 15

10 5 0 0 10 20 30 Time (s) 40 50 60 However, since we are accelerating, we do not take up all of that area. We can do 1 of two things. (y/x) corresponds they are the same

thing) 1. Divide the area by 2 2. Find the area of the triangle. The area under the line in a speed time graph equals the distance travelled Acceleration during the On time interval. a Bicycle 12 Speed (m/s) 10 8 6 4 2

0 0 10 20 30 Time (s) 40 50 60 Questions: 1. 2.

3. How can you tell from a speed-time table whether an object is accelerating? K (1) How can you tell from a speed-time graph whether an object is accelerating? K (1) Sketch a speed-time graph with two separate labelled lines for. C (2) 1. 2. 4. High positive acceleration Low negative acceleration . What feature of a speed time graph communicates K (2) 1. 2. The acceleration?

The distance? Two runners, Cathryn and Keir take part in a fundraising marathon. The graph below shows how their speeds change from the first 100 m from the start of the marathon. C (1) T (2) Which runner has the greater acceleration? Which runner is ahead after 100 s? Calculate and compare the distance travelled. Marathon Acceleration 7 Speed (m/s) 6

5 4 3 2 1 0 0 20 40 60 Time (s) 80 100 120

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