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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.

Verified Answer :

syed514

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)=40−2025=2025=45

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

facundo3141592

We want to find the mean acceleration of the car in the given time period.

The solution is x = 47.62

We know that first, Sarah's speed was 20 mph.

25 minutes after, her speed is 40mph.

By the mean value theorem, we know that if a function is differentiable in a given interval, then there exists a point on that interval such that the derivate of the function evaluated on that point is equal to the average rate of change of the function in that interval.

So what we need to find is the average rate of change of the velocity, which is given by:

ar = (final velocity - initial velocity)/time.

We will need to use the same units, because the velocity is in miles per hour, we need to write the time in hours.

We have:

time = 25 min,

And we know that:

1 hour = 60 min

then:

25 min = (25/60) hours = 0.42 hours.

Replacing the values we get:

ar = (40 mi/h - 20mi/h)/0.42h = 47.62 mi/h^2

Then the value of x that we want to determine is x = 47.62

If you want to learn more, you can read:

https://brainly.com/question/13264870

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