-2

I was reading a book and came across a formula which gives relativistic kinetic energy of a moving body with velocity $v=ßc$, where $c$ is speed of light. The formula is shown in image (equation number 1.12)

Relativisttic Energy

What I need to know is how for small values of ß, equation 1.12 becomes equation 1.13?

Qmechanic
  • 201,751
Manu Nair
  • 1
  • This book explains how old quantum theory was developed into new quantum mechanics and it explains how application of quantization in various fields of physics were done earlier. It is a part of equation. – Manu Nair Mar 16 '23 at 18:31
  • See https://physics.stackexchange.com/a/595175/123208 – PM 2Ring Mar 16 '23 at 19:12
  • The site standard for displaying mathematics is Mathjax. Posting images of text or mathematics is very strongly discouraged. – StephenG - Help Ukraine Mar 16 '23 at 19:32
  • 1
    A note, the letter in these equations is the Greek letter beta $\beta$ not the Germanic sharp s. Though this is neither here nor there. – Triatticus Mar 16 '23 at 21:20

1 Answers1

3

Taylor series to first order:

$$ \frac 1 {1-\epsilon} \approx 1 + \epsilon $$ $$ \sqrt{1 + \epsilon} \approx 1 + \frac 1 2 \epsilon $$

JEB
  • 33,420