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In the theory of relativity, the mass of a particle with speed $v$ is$$m=f(v)=\frac{m_{0}}{\sqrt{1-v^{2} / c^{2}}}$$where $m_{0}$ is the rest mass of the particle and $c$ is the speed of light in a vacuum. Find the inverse function of $f$ and explain its meaning.

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Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

Campbell University

Baylor University

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

0:00

In the theory of relativit…

03:17

00:57

02:55

01:39

Special Relativity. Einste…

05:37

The force $ F $ acting on …

02:37

Einstein found that an obj…

04:44

Relativity According to th…

02:58

Physics. The equation $m=m…

00:49

In the special theory of r…

So you have the bullying problem. Mom must off. I'm object. Moving bullion sp You know, relativity is a model by this question where not from us Erased particle of interests must sees the velocity of light. Thank you. So, uh, with his extreme verse, So, uh mm. It's a function off. The finding a numbers means that we want to fine fortune. The U S. Unfortunate for us. So that gives is there with us? So, in other words, we said, Well, muss are if he is gonna be ableto that expression and over square with one minus this quote over she squared. I don't want to find, uh, our velocity a PSA fortune on the b expressing terms of unless terms off. Okay, so your mom's too the soul for G desecration on this world on me, cancer is not heart will be easier, is there? So simply five, uh, so, uh, well began move. Usually there the Yeah, right. Multiplying right square with on both sides. So that's gonna give us quote one. My nose be squirt over. See, squirt is equal to and not for him. Right? So at this point, you can when it's squared up square both sides of the equation, so well, since this choir room always e this, uh, yeah, that's Mrs was eating number. Should people. So is gonna give us one lying us? Yeah. Article waas must be traveling at a smaller rescue than the speed of light. So that's gonna be pushing. So you have these, um, I'm going on at this point. What if Louise Well, that guy there, these run there. Uh, bye. So striking that both sides in the question not over him. Word on being RD on both sides of the question. The square. Where is he? Square. So, doing all that? We're gonna get one minus these. So it's obstructing that one. Minus him, Not over. Mmm. Or the squared should be equal to these. You're excited, too. Gets up. Sign the square. We're square. I'm going. At this point, you can take school. Exclude of that, they take square it. Well, the velocities are positive. So we're gonna get Oh, only the busty, this quote squirrel one. Oh, uh, I'm not divided by but one way. This I'm not. If I am, It's a word vehicle too. Over a seat. I've been at this point or move this year they're moving bloody both sides with you. So you gonna get that these velocity vehicle to see Time's up. So see, one mine does not over. So these didn't burst fortune. Oh, so orange is that if you plug into these your ma's, it gives you back the velocity. So, uh, what does it mean? That so it means, uh, well, so if you're going to these So to get, um, us, you have a must look, some us which velocity you should you should be. So if universal them, we'll give you but but which velocity? You should be traveling two. But being that must, it gives you that of us on there.

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