Average rate of change

Question

A rocket is 1 mile above the Earth in 30 seconds and 5 miles above the Earth in 150 seconds what is the Rockets rate of change in miles per second?

Answer 1

h=1 when t=30

h=5 when t=150

t =30h

h= t/30

the coefficient of t = 1/30 = the rate of change

rate of change = miles per second

= 1/30 mi/sec

=5mi/150 sec = 1/30 mi/sec

= .0333... miles per second

1 mile = 5280 feet

1/30 mi/sec = 5280/30 = 528/3 = 176 feet per second

= 58 2/3 yards per second

Answer 2

(5 - 1) / (150 - 30) = ?

Answer 3

Are we to assume the rocket began on surface level at 0 seconds?

If so, then from 0 seconds to 30 seconds, the rocket moved at:

(1 mile - 0 miles) ÷ (30 seconds - 0 seconds) = 1 mile / 30 seconds, or 1/30 miles/second

From 30 seconds to 150 seconds, the rocket moved at:

(5 miles - 1 mile) ÷ (150 seconds - 30 seconds) = 4 miles / 120 seconds, or 4/120 miles/second = 1/30 miles per second.

From 0 seconds to 150 seconds:

(5 miles - 0 miles) ÷ (150 seconds - 0 seconds) = 5 miles / 150 seconds, or 5/150 miles/second = 1/30 miles per second.

You can think of rate of change in miles per second as the “slope” the rocket moves at, so where it is now versus where it started from!