Question

The slope on a distance-time graph shows a ball moving from 20 m to 40 m in 1 s and from 40 m to 80 m in the next second

Answer 1

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:

• The distance covered is the change in the y-variable, so $\Delta y$
• The time elapsed is the change in the x-variable, so $\Delta x$

Speed is the ratio between distance and time, therefore

$speed = \frac{distance}{time}=\frac{\Delta y}{\Delta x}$

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

$distance = 40-20 = 20 m = \Delta y$

$time = 1 s = \Delta x$

So the slope in the first second is

$\frac{\Delta y}{\Delta x}=\frac{20}{1}=20 m/s$

In the next second, the ball moves from 40 m to 80 m, so

$distance = 80-40 = 40 m = \Delta y$

$time = 1 s = \Delta x$

So the slope in the next second is

$\frac{\Delta y}{\Delta x}=\frac{40}{1}=40 m/s$

While if we consider the overall graph in the 2 seconds, we have

$distance = 80-20 = 60 m = \Delta y$

$time = 2 s = \Delta x$

So the average slope is

$\frac{\Delta y}{\Delta x}=\frac{60}{2}=30 m/s$

Learn more about speed:

brainly.com/question/8893949

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