Project Math

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.