You drive on Interstate 10 from San Antonio to Houston, half the time at 65 km/h

Question

You drive on Interstate 10 from San Antonio to Houston, half the time at 65 km/h and the other half at 92 km/h. On the way back you travel half the distance at 65 km/h and the other half at 92 km/h.style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">

>type="text" name="rn_1363069_2_0_1368006" value="78.5" size="10" autocomplete="off" id="rn_1363069_2_0_1368006" dir="ltr">class="qtextfield">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">

The only part I need help with is finding the average velocity.style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">type="text" name="rn_1363069_2_0_1368006" value="78.5" size="10" autocomplete="off" id="rn_1363069_2_0_1368006" dir="ltr">class="qtextfield">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px; ">

You drive on Interstate 10 from San Antonio to Houston, half the time at 65 km/h and the other half at 92 km/h. On the way back you travel half the distance at 65 km/h and the other half at 92 km/h. What is your average speed for the entire trip? What is your average velocity for the entire trip?

Explanation / Answer

let the distance is d km

let t hours is the total time taken

d1 = 65*t/2 and d2 = 92*t/2

d = d1+d2

d = t*(65+92)/2 = t*78.5

Vav = d/t = t*78.5/t = 78.5 km/h



on the way back

let the distance is d km

let t hours is the total time taken

d/2 = 65*t1 ==> t1 = d/(2*65)

d/2 = 92*t2 ==> t2 = d/(2*92)

t = t1+t2 = (d/2)*(1/65 + 1/92) = (d/2)*(92+65 / 65*92)

Vav = d/t = 2*65*92 / (92+65) = 76.178 km/h




c) Vav = (76.178 + 78.5)/2 = 77.3 km/h

d) zero. since the displacement is zero

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