9.1 Speed
Speed is a rate of measure involving distance and time. It measures how fast an object moves per unit time.
Formula for Speed
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
Types of Speed
- Uniform Speed: An object has uniform speed if it travels equal distances in equal intervals of time.
- Non-Uniform Speed: An object has non-uniform speed if it travels unequal distances in equal intervals of time (or vice versa).
- Average Speed: Used when speed varies throughout a journey:
$$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$
Unit Conversions
- To convert $\text{km/h}$ to $\text{m/s}$: Multiply by $\frac{1000}{3600}$ (or divide by $3.6$).
- To convert $\text{m/s}$ to $\text{km/h}$: Multiply by $\frac{3600}{1000}$ (or multiply by $3.6$).
9.2 Acceleration
Acceleration is defined as the rate of change of speed with respect to time.
Formula for Acceleration
$$\text{Acceleration} = \frac{\text{Final Speed} - \text{Initial Speed}}{\text{Time Taken}} = \frac{v - u}{t}$$
Key Concepts
- Positive Acceleration: When speed increases over time ($v > u$).
- Deceleration (Negative Acceleration): When speed decreases over time ($v < u$).
- Zero Acceleration: When speed remains constant/uniform ($v = u$).
- SI Unit of Acceleration: Meters per second squared ($\text{m/s}^2$) or kilometers per hour squared ($\text{km/h}^2$).