4. Table 2.4 shows 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.
Table 2.4 Data for a sprinter during a race
Displacement
(m)
0 4 10 20 50 80 105
Time (s) 1 2 3 6 9 12
What about graph
I want to see answer
To draw the displacement-time graph, we will plot the given data points on a graph where the x-axis represents time (s) and the y-axis represents displacement (m).
The given data points are as follows:
Time (s): 1, 2, 3, 6, 9, 12
Displacement (m): 0, 4, 10, 20, 50, 80, 105
To plot these points, follow these steps:
1. Place the origin (0,0) at the bottom left corner of the graph.
2. Mark the time values on the x-axis: 1, 2, 3, 6, 9, 12.
3. Mark the displacement values on the y-axis: 0, 4, 10, 20, 50, 80, 105.
4. Plot the corresponding points on the graph:
- Point 1: (1, 0)
- Point 2: (2, 4)
- Point 3: (3, 10)
- Point 4: (6, 20)
- Point 5: (9, 50)
- Point 6: (12, 80)
- Point 7: (12, 105)
5. Connect these points with a continuous line.
To deduce the runner's speed in the middle of the race, we can calculate the slope of the line segment connecting the points in the middle of the race. In this case, we can calculate the slope between points 3 and 4, corresponding to time values 3 and 6.
The formula for the slope is:
Slope = (change in y) / (change in x)
Using points 3 and 4:
Displacement difference = 20 - 10 = 10 m
Time difference = 6 - 3 = 3 s
Slope = 10 m / 3 s ≈ 3.33 m/s
Therefore, the runner's speed in the middle of the race is approximately 3.33 m/s.
To draw a displacement-time graph, you can plot the time values on the x-axis and the displacement values on the y-axis.
First, let's plot the points from Table 2.4:
Time (s): 1 2 3 6 9 12
Displacement (m): 0 4 10 20 50 80 105
Now, let's draw a line connecting these points to create the graph. The line should pass through each point.
To deduce the runner’s speed in the middle of the race, we need to find the slope of the line at that point. In this case, the middle of the race is between the points (6, 20) and (9, 50).
To find the slope, we use the formula:
Slope = (change in displacement) / (change in time)
Change in displacement = 50 m - 20 m = 30 m
Change in time = 9 s - 6 s = 3 s
Slope = 30 m / 3 s = 10 m/s
Therefore, the runner’s speed in the middle of the race is 10 m/s.