Converting Seconds to MPHDate: 07/11/2000 at 19:54:16 From: Bob Subject: Seconds to MPH conversion CHART I'm looking for a chart that converts seconds traveled to miles per hour. I saw something in an FAQ about dividing by 3600. Thanks. Date: 07/12/2000 at 12:07:54 From: Doctor Rick Subject: Re: Seconds to MPH conversion CHART Hi, Bob. Could you specify the problem more carefully? You can't compute a speed (miles per hour) from a time (seconds) alone. Do you want, perhaps, times in seconds across the top and distances in feet down the side? Then the (average) speed is the distance divided by the time, and we need to convert feet to miles and seconds to hours. The division by 3600 converts seconds to hours; we similarly need to divide the distance in feet by 5280 to get the distance in miles. The whole formula for the problem as I stated it is D = distance in feet T = time in seconds S = speed in miles per hour S = (D/5280)/(T/3600) = (D/T)*(3600/5280) = (15/22)D/T You can use this formula in a spreadsheet to generate a table with the ranges of times and distances of interest to you. For instance, in Excel, a formula like =15/22*$B3/C$2 can be used to generate a table like 1 2 3 4 5 6 7 ------------------------------------------------------------- 1 0.682 0.341 0.227 0.170 0.136 0.114 0.097 2 1.364 0.682 0.455 0.341 0.273 0.227 0.195 3 2.045 1.023 0.682 0.511 0.409 0.341 0.292 4 2.727 1.364 0.909 0.682 0.545 0.455 0.390 5 3.409 1.705 1.136 0.852 0.682 0.568 0.487 6 4.091 2.045 1.364 1.023 0.818 0.682 0.584 7 4.773 2.386 1.591 1.193 0.955 0.795 0.682 8 5.455 2.727 1.818 1.364 1.091 0.909 0.779 9 6.136 3.068 2.045 1.534 1.227 1.023 0.877 10 6.818 3.409 2.273 1.705 1.364 1.136 0.974 11 7.500 3.750 2.500 1.875 1.500 1.250 1.071 12 8.182 4.091 2.727 2.045 1.636 1.364 1.169 13 8.864 4.432 2.955 2.216 1.773 1.477 1.266 14 9.545 4.773 3.182 2.386 1.909 1.591 1.364 15 10.227 5.114 3.409 2.557 2.045 1.705 1.461 16 10.909 5.455 3.636 2.727 2.182 1.818 1.558 where the numbers across the top are seconds and the numbers at the left are feet. Going 11 feet in 3 seconds comes out to 2.5 miles per hour. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 07/12/2000 at 12:16:22 From: Doctor Twe Subject: Re: seconds to MPH conversion CHART Hi Bob! Thanks for writing to Dr. Math! Unfortunately, seconds measures time and mph measures speed, so unless we have more information (a fixed distance traveled, for example) we can't convert seconds to mph. To convert seconds to hours, we divide by 3600 - that's where that number comes in. Let's say, for example, that we were measuring sprinters' times in the 100-yard dash and wanted to convert them to mph. We now have a fixed distance (100 yards), so we can calculate the speed. Let's say the sprinters ran it in 4.4 s, 4.6 s, 4.85 s and 5.2 s. s = d / t where: s = speed d = distance t = time So for the first sprinter, we have: s1 = 100 yd / 4.4 s = 22.73 yd/s Yards per second? Let's convert that to miles per hour. We can convert yards to miles by dividing by 1760 and, as mentioned above, we can convert seconds to hours by dividing by 3600. So we have: s1 = (100 yd / 1760 yd/mi) / (4.4 s / 3600 s/hr) = 0.0568 mi / 0.00122 hr = 46.49 mph Converting each measurement to miles and hours takes extra time. If we have more of the same calculations to do, we can incorporate the constants 1760 and 3600 (and even the 100 yds, if it doesn't change) directly into the formula with a little algebra: 100 yd ---------- 1760 yd/mi s = ---------------- t --------- 3600 s/hr 100 yd 3600 s/hr = ---------- * --------- 1760 yd/mi t 360000 mi = --------- 1760*t hr s = 204.54/t mph [or s = 2250/(11*t) mph for more accuracy.] Using this "condensed" formula, we can quickly convert the other sprinters' times into speeds: s2 = 204.54 / 4.6 = 44.47 mph s3 = 204.54 / 4.85 = 42.17 mph s4 = 204.54 / 5.2 = 39.34 mph I hope this helps! If you have any more questions, write back! - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ Date: 07/12/2000 at 15:33:50 From: Bob Hubert Subject: Re: seconds to MPH conversion CHART Thanks for the answer you provided. I think my question has complicated the issue. Let me be more specific and you tell me which formula is best. I thought it would be very simple to locate a chart in which the math has already been computed. If you travel 1 mile in 60 seconds, you are traveling 60 miles per hour. If you travel that mile in 55 seconds, what is your speed in MPH? I want a chart that people can carry in their cars so they do not depend upon their unreliable automobile speedometers. They can use a watch to time how many seconds it takes to travel from one milepost to another, then look at this chart to correctly determine their speed. I'm playing with the numbers and 3600 keeps coming into the equation. I'm so close but it is driving me a little nuts that I can't solve this. Thanks. Date: 07/12/2000 at 16:19:12 From: Doctor Rick Subject: Re: seconds to MPH conversion CHART Hi, Bob. Thanks for clarifying your question. If you had said "I'm looking for a chart that converts seconds IT TAKES TO TRAVEL ONE MILE to miles per hour," both Dr. TWE and I could have saved our effort. The formula is almost there in my response. Speed is distance divided by time. If the distance is 1 mile and the time is T seconds, then the time in hours is T/3600, and the speed is Speed = (1 mile)/(T/3600 hours) = 3600/T That's pretty simple; you just had it upside down. The table looks like this: Seconds MPH ------------ 36 100.0 37 97.3 38 94.7 39 92.3 40 90.0 41 87.8 42 85.7 43 83.7 44 81.8 45 80.0 46 78.3 47 76.6 48 75.0 49 73.5 50 72.0 51 70.6 52 69.2 53 67.9 54 66.7 55 65.5 56 64.3 57 63.2 58 62.1 59 61.0 60 60.0 61 59.0 62 58.1 63 57.1 64 56.3 65 55.4 66 54.5 67 53.7 68 52.9 69 52.2 70 51.4 71 50.7 72 50.0 73 49.3 74 48.6 75 48.0 76 47.4 77 46.8 78 46.2 79 45.6 80 45.0 81 44.4 82 43.9 83 43.4 84 42.9 85 42.4 86 41.9 87 41.4 88 40.9 89 40.4 90 40.0 91 39.6 92 39.1 93 38.7 94 38.3 95 37.9 96 37.5 97 37.1 98 36.7 99 36.4 100 36.0 101 35.6 102 35.3 103 35.0 104 34.6 105 34.3 106 34.0 107 33.6 108 33.3 109 33.0 110 32.7 111 32.4 112 32.1 113 31.9 114 31.6 115 31.3 116 31.0 117 30.8 118 30.5 119 30.3 120 30.0 121 29.8 122 29.5 123 29.3 124 29.0 125 28.8 126 28.6 127 28.3 128 28.1 129 27.9 130 27.7 131 27.5 132 27.3 133 27.1 134 26.9 135 26.7 136 26.5 137 26.3 138 26.1 139 25.9 140 25.7 141 25.5 142 25.4 143 25.2 144 25.0 - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 07/12/2000 at 17:44:55 From: Doctor Twe Subject: Re: seconds to MPH conversion CHART Hi again Bob! Thanks for writing back! As with the sprinters example, here we have a fixed distance. In this case, it's even easier than the 100 yards - it's exactly one mile! We can use the formula I gave previously to construct the chart: s = d / t Where: s = speed d = distance (1 mile) t = time (in seconds) Since the time is in seconds, we can convert it to hours by dividing it by 3600. But dividing the denominator (bottom of the fraction) by 3600 is the same as multiplying the numerator (top of the fraction) by 3600, so we get: 1 mi s = -------- (t/3600) 1 mi * 3600 = ----------- t s = 3600/t So to convert the time (in seconds) it takes to travel 1 mile to speed in mph, just divide 3600 by the number of seconds. As a chart, we have: Time Speed Time Speed Time Speed (s) (mph) (s) (mph) (s) (mph) ---- ----- ---- ----- ---- ----- 30 120 60 60 90 40 31 116 61 59 91 40 32 113 62 58 92 39 33 109 63 57 93 39 34 106 64 56 94 38 35 103 65 55 95 38 36 100 66 55 96 38 37 97 67 54 97 37 38 95 68 53 98 37 39 92 69 52 99 36 40 90 70 51 100 36 41 88 71 51 101 36 42 86 72 50 102 35 43 84 73 49 103 35 44 82 74 49 104 35 45 80 75 48 105 34 46 78 76 47 106 34 47 77 77 47 107 34 48 75 78 46 108 33 49 73 79 46 109 33 50 72 80 45 110 33 51 71 81 44 111 32 52 69 82 44 112 32 53 68 83 43 113 32 54 67 84 43 114 32 55 65 85 42 115 31 56 64 86 42 116 31 57 63 87 41 117 31 58 62 88 41 118 31 59 61 89 40 119 30 Using the formula above, you can extend this chart as necessary. Note that at higher speeds, the change in mph per second increases, so the margin of error also increases. Personally, I wouldn't put much stock in the reliability of this method. It relies on the precision of starting and stopping the watch at the precise moment you pass the mile marker (parallax becomes an issue), and the accuracy of the distance between the mileposts. Also, I'm not so sure it's a good idea to try to read your watch while driving - perhaps a passenger could do this. I hope this helps. If you have any more questions, write back again. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/ |
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