in this video we show how to measure the speed of a bicycle by using slow motion video from an
iphone we start with a quick reminder of constant velocity kinematics when the velocity of an object
is constant we can write distance equals rate times time or delta x equals v delta t note
that if we're keeping track of direction in this equation delta x should be called the displacement
that's how far something is moved in addition to a plus or minus sign to indicate direction
and v should be called velocity that's the speed with the plus or minus sign indicating
direction but in this video we're just going to work in magnitudes here and so i can say that
my delta x is really a distance it's just how far i went and my v is really a speed it's just
how fast i was going without using the plus or minus sign for direction so provided we have the
distance delta x and the time delta t we can solve for the speed here and the units we'll be using
our meters for the distance seconds for the time some meters per second and we'll do a conversion
to miles per hour at the very end so to find delta x we marked two points on a trail with
flagging tape and a line of chalk my finishing line is right there my starting line is right
there and we measured the separation distance out with the measuring tape at 5 meters plus or minus
a few centimeters so that's our delta x so i can be really conservative and say there's uncertainty
in the tenths place so we're going to write this to two significant digits as 5.0 meters but how
are we going to measure the time delta t to cross from the starting point to the finishing point
we decided to use slow motion video for this because the high frame rate of slow motion video
gives us a more precise measure of the time compared to ordinary speed video
but in order to figure out the time we have to count frames and use the frame rate of the
slow motion feature on our iphone to get to the frame rate on your phone go to settings
then camera then record slow-mo on my phone slow motion is recorded at 240 frames per second
and it's useful to flip that conversion factor around and say there's one second for every 240
frames i can then simplify the one over 240 and i find out there's about .004
seconds per frame so conservatively i'm going to say when i'm counting frames in this slow motion
video i might miss by up to two frames that would give me a little less than one hundredth
of a second uncertainty and again i'm just being conservative with the precision here
so i'm going to say my uncertainty in the time is 100 of a second so how do we go about converting
the total number of frames that we count into a time well suppose the total number of frames
is called n then what i do is take my n frames and i multiply by the conversion factor
one second for every 240 frames the units of frames are going to cancel out and leave me with
units of seconds all right next we open quicktime player and i can view my bike ride in slow motion
but i want to count the frames on this from when my front wheel touches the starting line
to when it touches the finishing line so to get frame count i go down to my timer in the
lower left hand corner just left click on that and switch it to frame number
now i can drag the video back and forth and you'll see that it's counting
what number frame it was so i'm going to go ahead and put my front tire on the starting line
and again there's a little bit of wiggle room here people could disagree on exactly which
frame it is but we're taking that into account with our uncertainty
i'm going to say my tire crossed that line at 111 frames then we fast forward to the finishing line
and i'm going to say my tire crossed that finishing line at 243 frames so we have
a number of frames from start to finish of 243 for the finish 111 for the start
and that gives me a total of 132 frames to cover 5 meters i take my 132 frames and i
multiply by my conversion factor one second for every 240 frames frames cancel out of this
and then i use a calculator to get 132 over 240. that comes out to 0.55 seconds now i
already decided that i had about a .01 second uncertainty so this is correctly rounded and i
have two significant digits finally we can get my speed and remember that our delta x was 5.0 meters
that's two significant digits our delta t is 0.55 seconds also two significant digits so when we get
our speed out of this we'll round it to two significant digits and that comes out to 9.1
meters per second finally i'd like to look at my speed in miles per hour since that's
the reference i'm used to and i use the conversion one meter per second
is 2.24 miles per hour so i take my 9.1 meters per second and i multiply by this conversion
factor in the correct order that's 2.24 miles per hour for every one meter per second the
meters per second cancel out and give me miles per hour and this gives me about 20.4 miles per hour
but it really should be rounding to two significant digits so i'm going to call it 20.
miles per hour so that's it on measuring the speed of an object with an iphone
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