All of the following would appear in an exemplary solution of the problem posed on the previous page.
Given:
Δx1 = 4.00 mi
Δx2 = 4.00 mi
v1 = 30.0 mi/h
v2 = 50.0 mi/h
Assumption: Ignore the amount of time it takes the car to speed up from 30.0 to 50.0 mi/h.
Goal: What is the average velocity, vav, for the trip?
For the first half of the trip, the elapsed time is
,
and for the second half, the elapsed time is
.
The total elapsed time is
,
and the average velocity for the entire trip is
.
Checks:
Units: mi/h = mi/(mi/(mi/hr))
Sign: The final result for average velocity is positive. That makes sense because positive was defined to the right.
Sense: The answer is closer to 30 mi/h than 50 mi/h. That makes sense, because the car spends more time at the lower speed.
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