# How to Calculate Velocity When you are not Given the Tim

Q:
How to calculate velocity when you are not given the time?
- Joe Jackson (age 21)
Namibia windhoek
A:

That's a toughie.   Usually you need a distance divided by time.  So you need a substitute for time, somehow.  The only thing I could come up with is to use a Doppler shift measurement.  If you are headed more or less toward a wall and emit a short burst of sound of known frequency and then measure the frequency of the reflected burst you can determine the relative velocity between the stationary wall and your velocity.

Let   β  =  V / Vs  where V is the velocity of the object and  Vs  is the velocity of sound.   let F be the frequency of the sound burst.   According to the usual Doppler formula, the wall will hear  FW = F(1 +  β).  The reflected sound will have  FR = FW (1 + β)  =  F (1 +  β)2 .    Solve for V.

Now you might nitpick and say,  well, somebody had to know the time in order to measure the velocity of sound but I'll leave that issue to philosophers.

LeeH

(published on 02/21/2017)

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