# GRE Physics GR 1777 Problem Solution¶

## 035. Relativity (Time Dilation)¶

### You should know¶

#### Time Dilation¶

$$\large t = \frac{t_0}{\sqrt{1-(v/c)^2}}$$

### Solution¶

A particle decays in 2.0$\mu$s $= 2.0 \times 10^{-6}$ s.

The particle moves at $v = 0.60 c$ in the lab frame, the time dilation is

$$\large t = \frac{2.0 \times 10^{-6}}{\sqrt{1-(3/5)^2}} = 2.5 \times 10^{-6} s$$

Therefore, before decaying, it will travel in the lab

$$\large d = (2.5 \times 10^{-6} s) \times (0.60 \times ( 3 \times 10^{10} m/s ))$$$$\large \therefore d = 450 m$$