What condition defines the Newtonian limit of special relativity?

What is the approximate value of \(\gamma\) when \(v\ll c\)?

State the first correction to \(\gamma\) for small \(\beta\).

Find \(\beta\) for a car moving at \(30.0\,\mathrm{m\,s^{-1}}\).

Estimate \(\gamma-1\) for \(v=30.0\,\mathrm{m\,s^{-1}}\).

Why is \(p=mv\) accurate for ordinary car speeds?

For \(v=0.100c\), estimate \(\gamma\) using \(1+\frac12\beta^2\).

For \(v=0.100c\), compare the relativistic kinetic energy approximation with \(\frac12mv^2\).

At \(v=0.0100c\), estimate the fractional correction to Newtonian momentum.

Use the low-speed limit to show that the Lorentz position transform becomes \(x'\approx x-vt\).

Use the low-speed limit to show that the Lorentz time transform becomes \(t'\approx t\).

Show that relativistic velocity addition becomes ordinary velocity subtraction at low speeds.

A particle moves at \(0.200c\). Estimate \(\gamma\) using the low-speed approximation and compare with the exact value.

At \(v=0.800c\), why is the Newtonian kinetic energy formula no longer reliable?

Explain why a successful new theory should reproduce older tested results in the appropriate limit.

Derive the low-speed kinetic-energy limit from \(K=(\gamma-1)mc^2\).

Derive the low-speed momentum limit from \(p=\gamma mv\).

Show that time dilation becomes negligible when \(v/c\) is very small.

Explain why rest energy does not appear in ordinary Newtonian kinetic-energy calculations.

A formula gives a finite massive-particle speed greater than \(c\) when pushed to high energy. What does that reveal about the formula?