Scenario:

travelling at 10 kmph and stopping every 30 meters for 3 seconds (always repeating this: start, stop, start, stop etc.)
for a total distance of 25 km

Question:

what is the formula used (most important) to work this out & how long would it take to complete the 25 km trip?


You might be able to guess what this scenario is, I'm trying to shut my boss up who is breaking my balls

Thank you in advance

not that difficult actually if you take the right approach

assuming that the average speed between those stops is 10 km/h in the following
which means your total travelling time is 2.5 hours ignoring the stops
now one has to work out the number of stops
25 km = 25,000 m
divide by 30 gives 833 1/3 which means 833 stops and then travel the last 10 m
833 x 3 = 2,499 seconds, subtract 1,800 seconds for 1/2 hour and you have 3 hours plus 699 seconds

so the total time from start to finish is 3 hours 11 minutes and 39 seconds

if you want a general formula rather than to work it out in two steps
that would be easy (try first yourself) only important to consider what to do if the distance is a multiple of the 30 m

ps: sounds like a junk mail distributor (the bikes used by posties in australia drive faster than 10 km/h)

This post was edited by brmv on Jul 13 2013 04:58am

if you assume instantaneous change in speed (0 - 10, 10 - 0) then it's straightforward. if you mean a real life scenario, you'll need to know the acceleration to speed up and slow down. and acceleration is prolly gonna change

As for the driving...

s = d/t therefore t =d/s. If s(driving)=10 km/hr, then t(driving) = d/10.

t(driving) = d/10

where t(driving) is given in hours and d is given in kilometers


For the stopping...

30 m = 30(10^-3) km

.... total number of stops is given by d/30(10^-3) where d is distance traveled in km.
.... the total time taken per stop is given by the number of stops multiplied by 3 seconds: t(stopping) = 3*(d/30(10^-3) = d/10(10^-3) = 100d.

NOTE: t(stopping) is in seconds and t(driving) is in hours; it would probably be more useful to convert t(stopping) into hours.

Therefore: t(stopping) = 100d* (1 min / 60 seconds) * (1 hr / 60 min)
After simplifying...

t(stopping) = d/36

where t(stopping) is in hours and d is in kilometers


Total time taken

Time is a function of distance.

t(total) = t(driving) + t(stopping)

t(d) = d/10 + d/36

where t(total) is in hours and d is in kilometers


Total time to drive 25 km

t(25) = (25)/10 + (25)/36 = 3.19 hours or 3 hours, 11 minutes, 40 seconds

This post was edited by travboat on Jul 14 2013 02:33pm

did you read my post?
you are off by 1 second because there is no 1/3 stop

thank you, that was helpful