Question

You drive on Interstate 10 from San Antonio to Houston, half the time at 62 km/h and the other half at 105 km/h. On the way back you travel half the distance at 62 km/h and the other half at 105 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip?

Answer #1

let time taken from san antonio to Houston = t

so total distance from san antonio to Houston = (t/2)*62 + (t/2)*105 = 83.5*t

a) average speed from san antonio to Houston = total distance / total time = 83.5*t/t = 83.5 km/h

b)

let total distance from houston to san antonio = d

total time taken from houston to san antonio = (d/2)/62 + (d/2)/105 = 0.01282*d

average speed = d/(0.01282*d) = 77.96 km/h

c)

average speed for entire trip = ( 83.5 + 77.96 ) / 2 = 80.73 km/h

d)

total displacement = 0

so average velocity = 0

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