1. **Problem:** A skateboarder moves straight along a sidewalk and covers 24 meters in 6 seconds. Find his horizontal velocity. 2. **Formula:** Velocity $v = \frac{\text{displacement}}{\text{time}}$ 3. **Calculation:** $$v = \frac{24}{6} = 4 \text{ m/s}$$ 4. **Explanation:** Velocity is displacement divided by time. Here, the skateboarder covers 24 meters in 6 seconds, so his velocity is 4 meters per second. --- 1. **Problem:** A ball is dropped from a 45 m building and falls for 2 seconds. Find its vertical position (displacement) from the point it was released. 2. **Formula:** Displacement under gravity $s = ut + \frac{1}{2}gt^2$, where initial velocity $u=0$ (dropped), $g=9.8$ m/s², $t=2$ s. 3. **Calculation:** $$s = 0 \times 2 + \frac{1}{2} \times 9.8 \times 2^2 = 0 + 0.5 \times 9.8 \times 4 = 19.6 \text{ m}$$ 4. **Explanation:** The ball falls 19.6 meters downward from the release point after 2 seconds. --- 1. **Problem:** A car initially moving at 10 m/s accelerates uniformly at 2 m/s² for 5 seconds. Find its final velocity. 2. **Formula:** Final velocity $v = u + at$, where $u=10$ m/s, $a=2$ m/s², $t=5$ s. 3. **Calculation:** $$v = 10 + 2 \times 5 = 10 + 10 = 20 \text{ m/s}$$ 4. **Explanation:** The car's velocity increases by $2$ m/s every second for 5 seconds, so final velocity is 20 m/s. --- 1. **Problem:** A toy car starts from rest and accelerates uniformly at 3 m/s² for 4 seconds. How far does it travel? 2. **Formula:** Displacement $s = ut + \frac{1}{2}at^2$, with $u=0$, $a=3$ m/s², $t=4$ s. 3. **Calculation:** $$s = 0 \times 4 + \frac{1}{2} \times 3 \times 4^2 = 0 + 1.5 \times 16 = 24 \text{ m}$$ 4. **Explanation:** Starting from rest, the toy car travels 24 meters in 4 seconds under uniform acceleration. **Final answers:** 1. Horizontal velocity = 4 m/s 2. Vertical displacement = 19.6 m 3. Final velocity = 20 m/s 4. Distance traveled = 24 m