Question

The Hubble Space Telescope orbits Earth at a constant speed. The graph below shows the relationship between x, time in seconds, and y, distance in kilometers. 1,000 900 800 700 600 500 400 300 200 100 0 20 40 60 80 100 x

Answer 1

When we have a graph with distance and time, the velocity will always be the slope of the graph, remember the definition of velocity

$v=\frac{\Delta S}{\Delta t}$

If S is on the y-axis and t on the x-axis it will be the same thing as the slope! Therefore we just need to find the slope of this line.

Looking at the graph we can see that at x = 40 we have y = 300, and x = 80 implies y = 600. Using the formula:

$\begin{gathered} v=\frac{600-300}{80-40} \\ \\ v=\frac{300}{40} \\ \\ v=\frac{30}{4} \\ \\ v=7.5\text{ km/s} \end{gathered}$

The velocity of the Hubble telescope is 7.5km/s

$v=7.5\text{ km/s}$