1. **State the problem:** We have a particle moving along a horizontal axis with position function $s = f(t) = 5t^2 - 2$. We want to find the velocity $v$ at time $t = 10$ seconds. 2. **Recall the formula:** Velocity is the rate of change of position with respect to time, so velocity $v(t)$ is the derivative of the position function $s(t)$: $$v(t) = \frac{ds}{dt} = f'(t)$$ 3. **Differentiate the position function:** $$f(t) = 5t^2 - 2$$ $$f'(t) = \frac{d}{dt}(5t^2) - \frac{d}{dt}(2) = 10t - 0 = 10t$$ 4. **Evaluate the velocity at $t=10$:** $$v(10) = 10 \times 10 = 100$$ 5. **Interpretation:** The velocity of the particle at 10 seconds is $100$ meters per second.