1. What is Speed?
Speed is the distance covered by an object in unit time:
$$\mathbf{\text{Speed} = \frac{\text{Distance Travelled}}{\text{Time Taken}} \quad \left(v = \frac{d}{t}\right)}$$
• SI Unit: meters per second ($\text{m/s}$)
• Commercial Unit: kilometers per hour ($\text{km/h}$)
$$\mathbf{1\text{ km/h} = \frac{1000\text{ m}}{3600\text{ s}} = \frac{5}{18}\text{ m/s}} \quad \text{and} \quad \mathbf{1\text{ m/s} = \frac{18}{5}\text{ km/h} = 3.6\text{ km/h}}$$
2. Uniform vs. Non-Uniform Motion
- Uniform Motion: An object moving along a straight line covering equal distances in equal intervals of time (constant speed; straight-line distance-time graph).
- Non-Uniform Motion: An object whose speed changes, covering unequal distances in equal intervals of time (e.g. a car in city traffic; curved distance-time graph). Here, we calculate Average Speed: $$\mathbf{\text{Average Speed} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}}}$$
3. Concrete Worked Example
Example: A Rajdhani Express train covers $360\text{ km}$ in $4\text{ hours}$. Calculate its speed in $\text{km/h}$ and in $\text{m/s}$.
$$\text{Speed} = \frac{360\text{ km}}{4\text{ h}} = \mathbf{90\text{ km/h}}$$
Convert to $\text{m/s}$: $90 \times \frac{5}{18} = 5 \times 5 = \mathbf{25\text{ m/s}}$.