posted by ben .
You drive on an interstae 10 from San Antonio to Huston, half the [b]time[/b] at 55km/h and the other half at 90km/h. On the way back you travel half the [b]distance[/b] at 55km/h and the other half at 90km/h.
What is your average speed from San Antonio to Houston
What is your speed from houston to San Antonio?
c) speed for entire trip
d) What is your average velocity for the whole trip?
Let T = total time of trip and D = toal distance covered
average speed = distance/time
(a) SA to Houston:
V1 = 55*(T/2)+90*(T/2) / T = (55+90)/2) = ?
(b) Houston to SA:
V2 = D/[(D/2)(1/55)+(D/2)(1/90)]
= 2/[(1/55) + (1/90)]
(c) 2D/[D/V1 + D/V2]=
2/[1/V1 = + 1/V2)]
(d) Think about the definition of velocity. You end up where you started in this case. Vector displacement = 0.