A spaceship travels at $v = 0.6c$ relative to Earth. A clock on the spaceship ticks for $\tau_0 = 10$ s (proper time). Find the time elapsed on Earth (time dilation).

$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} = \frac{1}{\sqrt{1-0.36}} = \frac{1}{\sqrt{0.64}} = \frac{1}{0.8} = 1.25$$

$$\Delta t = \gamma \tau_0 = 1.25 \times 10 = 12.5 s$$

More time elapses on Earth — confirming the moving clock runs slow.