1. **Problem Statement:** A car accelerates from rest at a constant rate of $3\ \text{m/s}^2$ for $5$ seconds. Calculate the final velocity and the distance traveled during this time. 2. **Formulae and Rules:** - Final velocity: $v = u + at$ - Distance traveled: $s = ut + \frac{1}{2}at^2$ - Initial velocity $u = 0$ since the car starts from rest. 3. **Calculations:** - Final velocity: $v = 0 + 3 \times 5 = 15\ \text{m/s}$ - Distance traveled: $s = 0 \times 5 + \frac{1}{2} \times 3 \times 5^2 = \frac{1}{2} \times 3 \times 25 = 37.5\ \text{m}$ 4. **Explanation:** The car starts from rest, so initial velocity is zero. Using the constant acceleration formulas, we find the final velocity after $5$ seconds and the total distance covered in that time. **Final answers:** - Final velocity: $15\ \text{m/s}$ - Distance traveled: $37.5\ \text{m}$