Suppose v(t) = 500 − 25t represents the speed in meters per second of an
airplane after t seconds. Here v(t) the speed after t seconds. Find and discuss
the meaning, in the context of this application, of the intercepts of the vertical
and horizontal axes.

The y-intercept is (0,500).

Interpretation :

The initial velocity is 500 meters per seconds.

The x-intercept is (20,25)

Interpretation :

When the time is 20 seconds the velocity is 0 meters per second.

Note that : I have written the intercept points.

Please ask if you have any confusion.

Step-by-step explanation

The velocity function is

v(t)=500−25t

y-intercept :

For t=0 we have v(0)=500−25×0=500.

So, the y-intercept is (0,500).

Interpretation :

The initial velocity is 500 meters per seconds.

x-intercept :

For v(t)=0 we have

500−25t=0

⇒25t=500

⇒t=20

So, the x-intercept is (20,0)

Interpretation :

When the time is 20 seconds the velocity is 0 meters per second.