1. **State the problem:** A car accelerates from an initial speed $v_0 = 15$ m/s to a final speed $v = 25$ m/s over a distance $d = 125$ m. We need to find the time $t$ it takes to reach the final speed. 2. **Formula used:** We use the kinematic equations for constant acceleration. The key formulas are: $$v = v_0 + at$$ $$v^2 = v_0^2 + 2ad$$ where $a$ is acceleration, $t$ is time. 3. **Find acceleration $a$:** From the second formula, $$a = \frac{v^2 - v_0^2}{2d} = \frac{25^2 - 15^2}{2 \times 125} = \frac{625 - 225}{250} = \frac{400}{250} = 1.6 \text{ m/s}^2$$ 4. **Find time $t$:** Using the first formula, $$t = \frac{v - v_0}{a} = \frac{25 - 15}{1.6} = \frac{10}{1.6} = 6.25 \text{ seconds}$$ **Final answer:** The car takes $6.25$ seconds to reach the final speed of 25 m/s.