You drive on Interstate 10 from San Antonio to Houston, half the time at 54 km/h

Question

You drive on Interstate 10 from San Antonio to Houston, half the time at 54 km/h and the other half at 85 km/h. On the way back you travel half the distance at 54 km/h and the other half at 85 km/h.
(a) What is your average speed from San Antonio to Houston?
____________ km/h

(b) What is your average speed from Houston back to San Antonio?
___________ km/h

(c) What is your average speed for the entire trip?
__________ km/h

(d) What is your average velocity for the entire trip?
____________ km/h

(e) Describe in words the graph x versus t for (a), assuming the motion is all in the positive x direction.
5

(f) Describe how the average velocity can be found on a graph of x versus t.

Explanation / Answer

average speed=(total distance traveled)/(total time taken) assume distance between San Antonio and Houston=d a) average speed from San Antonio to Houston=d/{[(d/2)/54]+[(d/2)/85]} =2*54*85/(54+85) =66.04 kmph b)average speed from San Antonio to Houston=d/{[(d/2)/54]+[(d/2)/85]} =2*54*85/(54+85) =66.04 kmph c)average speed for the entire trip=2d/{[(d/2)/54]+[(d/2)/85]+[(d/2)/54]+[(d/2)/85]} =2*54*85/(54+85) =66.04 kmph d)average velocity for the entire trip=(total displacement)/(total time taken) but total displacement =0(since we reached where we started) ==>average velocity for the entire trip=0 kmph e)the equation of x vs t for first half of San Antonio to Houston==>x=54t. the equation of x vs t for second half of San Antonio to Houston==>x=85t. the equation of x vs t for first half of Houston back to San Antonio==>x=54t. (actually there must be a negative sign but given assumption in the problem that take the motion is all in the positive x direction) the equation of x vs t for second half of Houston back to San Antonio==>x=85t.

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