Question

Sarah is driving her car very smoothly from
Austin to Dallas one day. At 6:00 pm she is
travelling at 20 mph, while 25 minutes later
she is travelling at 40 mph.
Calculus tells us that at some time between
6:00 pm and and 6:25 pm her acceleration is
exactly x mph/h. Determine x.

Answer 1

this is the mean value theorem

Answer 2

like saying
\[v(0)=20, v(25)=40\] and so by mean value theorem there is an x between 0 and 25 with
\[v'(x)=\frac{40-20}{25}=\frac{20}{25}=\frac{4}{5}\]]

Answer 3

and since the derivative of the velocity is the acceleration, that is your answer

Answer 4

Yeah. What satellite says. 4/5 mph/min
but we want x in mph/h, so multiply by 60
(4/5)*60=48 mph/h

Answer 5

Thanks both ya

Answer 6

oh good point!