Answer: 6.2 cm
Explanation:
Here we need to integrate the given graph to find the total distance moved by the blood.
We have two lines, one with the points:
(0.1s, 0m/s) and (0.15s, 0.8 m/s)
remember that:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then the slope for this line is:
a = (0.8m/s - 0m/s)/(0.15s - 0.1s) = 1.6 m/s^2
y = (1.6m/s^2)*x + b
To find the value of b we can just replace the values of one of the points, like (0.1s, 0m/s)
0m/s = (1.6m/s^2)*0.1s + b
0m/s = 0.16m/s + b
b = -0.16m/s
Then the equation is:
y = (1.6m/s^2)*x -0.16m/s
Now we integrate this between x = 0.1s and x = 0.15s
distance = (1/2)*(1.6m/s^2)*((0.15s)^2 - (0.1s)^2) - (0.16m/s)*(0.15s - 0.1s)
distance = 0.002m
Now we need to see the distance moved in the other part of the graph.
This line has the points:
(0.15s, 0.8 m/s) and (0.3s, 0m/s)
Then the slope of this line is:
a = (0m/s - 0.8m/s)/(0.3s - 0.15s) = -5.33m/s^2
y = (-5.33m/s^2)*x + b
Now we replace the values of one of the points, like (0.3s, 0m/s)
0m/s = (-5.33m/s^2)*0.3s + b
b = 5.33m/s^2*0.3s = 1.6m/s
Then the equation for this line is:
y = (-5.33m/s^2)*x + 1.6m/s
Now we integrate this between x = 0.15s and x = 0.3s
distance = (1/2)*(-5.33m/s)*( (0.3s)^2 - (0.15s)^2) + (1.6m/s)*(0.3s - 0.15s)
distance = 0.06m
Then the total distance moved is:
D = 0.06m + 0.002m = 0.062m
And we want this in cm, remember that 1m = 100cm
D = 0.062m = 0.062*100cm = 6.2 cm
