Slope in the first second: 20 m/s
Slope in the next second: 40 m/s
Average slope: 30 m/s
Explanation:
On a distance-time graph, the slope of the curve represents the speed of the object.
In fact, we have:
Speed is the ratio between distance and time, therefore
[tex]speed = \frac{distance}{time}=\frac{\Delta y}{\Delta x}[/tex]
which corresponds to the slope of the line.
In this problem, we have a ball moving from 20 m to 40 m in 1 s, so
[tex]distance = 40-20 = 20 m = \Delta y[/tex]
[tex]time = 1 s = \Delta x[/tex]
So the slope in the first second is
[tex]\frac{\Delta y}{\Delta x}=\frac{20}{1}=20 m/s[/tex]
In the next second, the ball moves from 40 m to 80 m, so
[tex]distance = 80-40 = 40 m = \Delta y[/tex]
[tex]time = 1 s = \Delta x[/tex]
So the slope in the next second is
[tex]\frac{\Delta y}{\Delta x}=\frac{40}{1}=40 m/s[/tex]
While if we consider the overall graph in the 2 seconds, we have
[tex]distance = 80-20 = 60 m = \Delta y[/tex]
[tex]time = 2 s = \Delta x[/tex]
So the average slope is
[tex]\frac{\Delta y}{\Delta x}=\frac{60}{2}=30 m/s[/tex]
Learn more about speed:
brainly.com/question/8893949
#LearnwithBrainly
