QR question with distance, time and speed

[dentalstudent2021]

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Hello guys,
question : Valerie drives on the highway at a speed of 60 mph for 15 minutes and then 45 mph on the local roads for 20 minutes. what is her Average velocity ?

I understand that avg velocity = total dist / total time.

But why can't we take the avg of both the speed ? - (speed 1 + speed 2) / time ?

Thanks

 

[FeralisExtremum]

We calculate average velocity as total distance and total time, not simply averaging the two velocities.

To use an extreme example, let's say you have a 2 mile trip. You travel the first mile at 1 mph and you travel the second mile at 999 mph. Is your average velocity for the trip 500 mph? Of course not, because you spent an hour traveling the first half of the trip alone. If your average speed was actually 500 mph, the entire two mile trip would have taken you less than half a minute. Demonstrably, we can see that the arithmetic average of velocities is not valid in these situations.

Hope that helps - let me know if you need additional explanation. You can't simply take the averages because you spent differing amounts of time at each speed, and traveled different distances for each. They can't be assumed to weigh equally in contributing to the overall trip.

 

[dentalstudent2021]

Hope that helps - let me know if you need additional explanation. You can't simply take the averages because you spent differing amounts of time at each speed, and traveled different distances for each. They can't be assumed to weigh equally in contributing to the overall trip.

Thank you. Makes it clear.

 

[DAT Destroyer]

Hello guys,
question : Valerie drives on the highway at a speed of 60 mph for 15 minutes and then 45 mph on the local roads for 20 minutes. what is her Average velocity ?

I understand that avg velocity = total dist / total time.

But why can't we take the avg of both the speed ? - (speed 1 + speed 2) / time ?

Thanks

The average speed is: total distance/total time not (v1 + v2)/2 which is the arithmetic average of the speeds.


Note: this is a VERY common mistake.

Hope this helps