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    To find the average speed of 2 different speeds, why can't you just add them, then divide by 2? PLS HELP
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    you can
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    (Original post by Big_man_conor)
    you can
    Oh no you can't.

    If you go at 10m/s for 10s and then 20m/s for only 2s, the average ain't going to be 15m/s

    You need to find the total distance travelled and divide by the total time taken.
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    If you're talking about a journey where one person travels at two different speeds during phases of a journey, then you have to take into account how long they have travelled for.
    For example, if I walked 100m at 0.5m/s and then ran 10m at 2m/s then my average speed wouldnt be (0.5+2)/2= 1.25m/s because then the total journey would have taken (110/1.25)= 88 seconds when in reality it took 100m/0.5=200 seconds for the walk AND 10/2=5 seconds for the run for a total of 205 seconds.
    So, 205 seconds to go 110 metres. average Speed=distance/time=110/205 which is equal to 0.5366m/s

    Hope this helps
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    (Original post by tomkeeling)
    if you're talking about a journey where one person travels at two different speeds during phases of a journey, then you have to take into account how long they have travelled for.
    For example, if i walked 100m at 0.5m/s and then ran 10m at 2m/s then my average speed wouldnt be (0.5+2)/2= 1.25m/s because then the total journey would have taken (110/1.25)= 88 seconds when in reality it took 100m/0.5=200 seconds for the walk and10/2=5 seconds for the run for a total of 205 seconds.
    So, 205 seconds to go 110 metres. Average speed=distance/time=110/205 which is equal to 0.5366m/s

    hope this helps
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    (Original post by BeepBopBoop)
    To find the average speed of 2 different speeds, why can't you just add them, then divide by 2? PLS HELP
    You're question is slightly ambiguous. But I'll take it to mean two different speeds over two different time intervals.

    It depends on how long the time interval is where you're traveling at a certain speed. The average will skew towards the speed at which you were travelling for the longest distance, if you have constant speeds.

    If the velocity is a continuous function then

    Using velocity  \mathBB{v(t)}.

    There is an "average value theorem" which says the average value of a function is \displaystyle \frac{1}{b-a} \int^{b}_{a} f(x)dx

    so taking velocity as above the average speed over time interval (a,b) is \displaystyle \frac{1}{b-a} \int^{b}_{a} \mathBB{v(t)}dt

    Now; in probability, you know the average (arithmetic mean) is the sum of a collection divided by the entire count in a set. For example if there are numbers 15 , 16 ,17 ,18. you know the average is when you add them and then divide by 4. the average is 16.5

    It's an analagous argument with average speed. This suggests the average speed will be total-speed/time. But the difference is the speed is changing with time.

    So we could take the speed for each 10 seconds add them, like we did with the numbers and then divide by the total time, but then what happens if the speed changes in 5 seconds ? 1 second or 0.02 seconds ?

    Then we take the limiting value as t tends to 0, hence why the integrals come into play (thinking of it as the limit of a sum).
 
 
 
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