You drive on Interstate 10 from San Antonio to Houston, half thetime at 51 km/h
ID: 1663886 • Letter: Y
Question
You drive on Interstate 10 from San Antonio to Houston, half thetime at 51 km/h and the otherhalf at 70 km/h. On the way backyou travel half the distance at51 km/h and the other half at 70 km/h. (a) What is your average speed from San Antonio toHouston?km/h
(b) What is your average speed from Houston back to SanAntonio?
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
(a) What is your average speed from San Antonio toHouston?
km/h
(b) What is your average speed from Houston back to SanAntonio?
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
Explanation / Answer
(a) What is your average speed fromSan Antonio to Houston?Vavg1 = [V1t1 +V2t2] / [t1 +t2] where ttotal1=[t1 + t2] Vavg1 = [51 x 0.5 + 70x0.5] /[0.5 + 0.5]
Vavg1 = 60.5 km/h
(b)What is your average speed from Houston back to SanAntonio?
Vavg2 = [V3t3 +V4t4] / [t3 + t4] where ttotal2= [t3 +t4]
t3 = V3/(0.5 S ) ; t4 =V4/(0.5 S )
t3 = 0.5 S /V3 ; t4 =0.5 S /V4
Vavg2 = [V3 0.5 S /V3 + V4 0.5 S /V4] / [0.5 S/V3 + 0.5 S/V4 ]
Vavg2 = [1 + 1] / [1/V3 + 1/V4 ]
Vavg2 =2 [V3 V4 ] /[V3 + V4 ]
Vavg2 = [ 51x70 ] / [51+ 70]
Vavg2 = 59.0 km/h
(c) What is your average speed for the entiretrip?
Vavg = [Vavg1ttotal1 +Vavg2ttotal2 ] /[ttotal1 +ttotal2] ttotal1 = S/Vavg1 ttotal2= S/Vavg2 wehave Vavg =[Vavg1 S/Vavg1 +Vavg2 S/Vavg2 ] /[S/Vavg1 +S/Vavg2 ] Vavg = [1 + 1 ] /[1/Vavg1 + 1/Vavg2 ] Vavg= 2[Vavg1 Vavg2 ] / [Vavg1 + Vavg2 ]
Vavg =2[60.5x 59 ] / [60.5 + 59.0 ]
Vavg = 59.75km/h (d) What is your average velocity forthe entire trip?
Zero (0) since you have returned back to San Antonio and yourdisplacement was 0.