Subjects physics

Uniform Acceleration 629F21

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1. **Problem Statement:** A car accelerates uniformly from 18 km/h to 36 km/h in 5 seconds. We need to find: i) The acceleration ii) The distance covered in that time 2. **Convert units:** Since acceleration and distance calculations require consistent units, convert speeds from km/h to m/s. $$u = 18 \times \frac{1000}{3600} = 5 \text{ m/s}$$ $$v = 36 \times \frac{1000}{3600} = 10 \text{ m/s}$$ 3. **Formula for acceleration:** $$v = u + at$$ Rearranged to find acceleration: $$a = \frac{v - u}{t}$$ 4. **Calculate acceleration:** $$a = \frac{10 - 5}{5} = \frac{5}{5} = 1 \text{ m/s}^2$$ 5. **Formula for distance covered:** $$s = ut + \frac{1}{2}at^2$$ 6. **Calculate distance:** $$s = 5 \times 5 + \frac{1}{2} \times 1 \times 5^2 = 25 + \frac{1}{2} \times 25 = 25 + 12.5 = 37.5 \text{ meters}$$ **Final answers:** - Acceleration $a = 1$ m/s$^2$ - Distance covered $s = 37.5$ meters