Show how the displacement of a runner changed during a sprint race.draw a displacement-time graph to show this data, and use it to deduce the runner's speed in the middle of the race.
Displacement (m) 0 4 10 20 50 80 105,
Time(s) 0 1 2 3 6 9 12.
Grade 9
He is not running at constant speed.
Notice that he goes 4 meters in the first second and 6 meters in the second second
speed versus time
change in distance/change in time
4/1 = 4
(10-4) /1 = 6
(20-10)/1 = 10
(50-20)/3 = 10
(80-50)/3 = 10
(105-80)/3 = 25/3 = 8 1/3
looks like 10 m/s is speed in the middle
Draw the displacement_time graph of this
To draw displacement time graph
To create a displacement-time graph, you need to plot the given data points on a graph. The displacement values (in meters) will be plotted on the y-axis, and the time values (in seconds) will be plotted on the x-axis. Since the given data is discrete, you will be plotting individual points and connecting them to form a line.
Looking at the given data:
Displacement (m): 0 4 10 20 50 80 105
Time (s): 0 1 2 3 6 9 12
Plotting these data points on a graph, you will get the following points:
(0, 0), (1, 4), (2, 10), (3, 20), (6, 50), (9, 80), (12, 105)
Now, connect these points to create a line graph. The resulting graph should look something like this:
|
120 | * (12,105)
|
100 |
|
80 | * (9,80)
|
60 |
|
40 | * (6,50)
|
20 | * (3,20)
|
0 * (0,0) * (1,4) * (2,10)
Now, to deduce the runner's speed in the middle of the race, we can observe the slope of the line segment between the data points representing a time interval.
Looking at the graph, we can focus on the line segment between points (3, 20) and (6, 50). The time interval between these points is 6 - 3 = 3 seconds, and the displacement change is 50 - 20 = 30 meters.
To calculate the speed, which is the rate of change of displacement with respect to time, we can use the formula:
Speed = Displacement change / Time interval
In this case, the speed is:
Speed = 30 meters / 3 seconds = 10 meters per second
Therefore, the runner's speed in the middle of the race is calculated to be 10 meters per second.