at a speed of 65 km/h?
2007-09-13 16:31:16 · 5 answers · asked by abbs 2 in Science & Mathematics ➔ Physics
Your average velocity is 55.221... km/hr.
It is NOT the simple average or mean of 48km/h and 65km/h, because in driving the same distances, speed and time taken have an INVERSE relationship.
(The naive idea that you just take the average of the speeds under such circumstances is a COMMON MISCONCEPTION!)
226 km at 48 km/h takes you 226/48 h = 4.70833... h.
226 km at 65 km/h takes you 226/65 h = 3.47692... h.
So the total 452 km take you 8.18526... h, and thus your AVERAGE SPEED = 452 km / 8.18526... h
= 55.221... km/h.
The lesson worth learning here is that when driving equal distances at two different speeds, your AVERAGE SPEED will always be LESS that the average of your two different speeds.
ONLY if you drive at two different speeds for the SAME TIME is your average speed equal to the average of those two speeds. (That is because the distance travelled and the speed you're travelling at then have a DIRECT rather than an INVERSE relationship.)
Live long and prosper.
P.S. For those more mathematically minded, two given numbers have at least three kinds of "mean," their arithmetic, their geometric, or their harmonic mean. The average speed when driving equal distances at two different speeds 'a' and 'b' involves the "harmonic mean" 'hm,' defined by
1/a + 1/b = 2/hm.
You can readily check this out by substituting a = 48 and b = 65. You will find that hm = 55.221..., as already found above. QED
2007-09-13 16:52:29 · answer #1 · answered by Dr Spock 6 · 0⤊ 0⤋
Since distances are the same, & speeds are constant,
average velocity is (48 + 65)/2 = 56.5 km/hr.
2007-09-13 23:37:10 · answer #2 · answered by Robert S 7 · 0⤊ 0⤋
aveg. velocity = total displacement / total time
total displacement is 226 + 226 = 452km
total time is 226/48 + 226/65
aveg. velocity = (452km) / ( 226/68 + 226/65)
aveg. velocity = 55.22 km/hr
2007-09-14 00:19:32 · answer #3 · answered by 7 · 0⤊ 0⤋
Average velocity = Total Distance / Total time taken
Total Dist. = 226km x 2 = 452 km
Total time taken = 226/48 + 226/65= 4.708+3.477=8.185Hr
Ave. Velo. = 452 / 8.185=55.22 kmph
...............................===============
2007-09-14 01:25:18 · answer #4 · answered by Joymash 6 · 0⤊ 0⤋
i think it depends on your weight and the traffic situation
2007-09-13 23:39:30 · answer #5 · answered by Anonymous · 0⤊ 0⤋