Signal is sent, then it comes back, the time is measured. Then the second time.
d1d2=speed⏟know⋅time⏟measure=speed⋅time
Reading comes from the following:
d2−d1Time between signals.
To get an idea, consider this extreme example: what if you are just passing the cop's car, like this?
Reading =
0. So, the reading might be off...
Since 80 m/h is your speed,
dPdt=80. That's what the cop wants to know. But what does the radar measure in reality?
dSdt.
P2+D2=S2←Not numbers, variabes, i.e.,functions.
This connects
P and
S, not
dPdt and
dSdt yet. We differentiate Pythagoras Theorem with respect to
t to get there:
ddt(P2+D2)ddt(P2)+ddt(D2)2P⋅dPdt+2DdDdt⏟=0P⋅dPdt∴dSdt=ddt(S2)=ddt(S2)=2S⋅dSdt=S⋅dSdt=PSdPdt
We have a relation between these four functions of
t:
dSdt=PSdPdt.
