 guringpw

2022-01-06

A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to a patrol officer 30 mi along the highway. When the car reached the location of the second officer 28 min later, it was clocked going $60\frac{mi}{hr}$. The driver of the car was given a ticket for exceeding the $60\frac{mi}{hr}$ speed limit Why can the officer conclude that the driver exceeded the speed limit? zesponderyd

We know that the speed is calculated as the ratio of the distance with time. From the Mean Value Theorem, we conclude that if the average speed is greater than the speed limit, then at some point we must have exceeded the speed limit In order to answer the question if the driver has exceeded the speed limit or not, we have to alculate the average speed. Since the time is given in minutes, we have to convert it in hours by dividing it by 60.
${v}_{avg}=\frac{30-0}{\frac{28}{60}-0}\approx 64.3\frac{mi}{h}$ Elaine Verrett

Step 1
We know that
$speed=\frac{distance}{time}$
From the mean value theorem, we can say that if the average speed is greater than the speed limit, then at some point, we must have exceeded the speed limit.
Here we have to calculate the average speed, to know whether the driver has exceeded the speed limit or not.
We convert the time into hours by dividing the given time by 60, since the given time is in minutes.
Step 2
${v}_{avg}=\frac{30-0}{\frac{28}{60}-0}\approx 64.3\frac{miles}{hr}$
This shows that driver has exceeded the speed limit. karton

Step 1
Tt is given that the car was travelling at a speed of $60\frac{mi}{hr}$ at the location of second officer.
The driver of the car was given a ticket for exceeding the speed limit of $60\frac{mi}{hr}$.
The officer can conclude that the driver exceeded the speed limit, by calculating the average speed of the car.
Step 2
Average $speed=\frac{{d}_{2}-{d}_{1}}{{t}_{2}-{t}_{1}}$
$=\frac{\left(30-0\right)mi}{\left(\frac{28}{60}-0\right)hr}$ ($\therefore$ initial distance ${d}_{1}=0$ and at rest ${t}_{1}=0$)
$\approx 64.28\frac{mi}{hr}$
As the average speed is $64.28\frac{mi}{hr}$, the driver has exceeded the speed limit.

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