Hello! I'm teaching some physics and I need some help with this equation :)

[BobcatIon]

I'm trying to work out how to simplify? this:

C² = (4D²/Δt²) + v²

to

Δt = 2D / (c*sqrt(1 – v²/c²)

 

[Deleted member 4993]

I'm trying to work out how to simplify? this:

C² = (4D²/Δt²) + v²

to

Δt = 2D / (c*sqrt(1 – v²/c²)

Start with subtracting v² from both sides of the given equation. Then isolate t² and take squareroot.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[HallsofIvy]

I suspect that your problem is with that \(\displaystyle \sqrt{1- \frac{v^2}{c^2}}\). It is fairly easy to get to \(\displaystyle \frac{4D^2}{\Delta t^2}= c^2- v^2\) and then \(\displaystyle \frac{2D}{\Delta t}= \sqrt{c^2- v^2}\).

Now write \(\displaystyle c^2- v^2= c^2- c^2\left(\frac{v^2}{c^2}\right)\) so you can factor \(\displaystyle c^2\) out of \(\displaystyle c^2- v^2= c^2\left(1- \frac{v^2}{c^2}\right)\). Finally, take the square root: \(\displaystyle \sqrt{c^2- v^2}= \sqrt{c^2\left(1- \frac{v^2}{c^2}\right)}= c\sqrt{1- \frac{v^2}{c^2}}\).