ANAND CLASSES study material and notes which explore the concept of Speed with detailed explanations, formulas, SI units, dimensional analysis, types of speed, graphical representation, relative speed, and real-life applications. Includes FAQs, MCQs, conceptual questions, worksheets, and a test paper for JEE, NEET, and CBSE Class 11 exams.
Introduction to Speed
Every moving object has some measure of motion. The rate at which an object covers distance determines how fast or slow it moves.
Definition:
Speed is the rate at which an object moves and is defined as the distance covered per unit time.
Mathematical Expression:
\begin{array}{l} \text{Speed} = \frac{\text{Distance Travelled}}{\text{Time Taken}} \end{array}
Understanding Speed with a Simple Example
Imagine two people walking:
- Person A covers 100 m in 20 seconds.
- Person B covers 100 m in 10 seconds.
The speed of Person A: \begin{array}{l} v = \frac{100}{20} = 5 \text{ m/s} \end{array}
The speed of Person B: \begin{array}{l} v = \frac{100}{10} = 10 \text{ m/s} \end{array}
Since Person B has a higher speed, they move faster than Person A.
Types of Speed
1. Uniform Speed
- When a body covers equal distances in equal time intervals, it is said to be moving with uniform speed.
- Example: A car moving at a constant speed of 60 km/h on a highway.
2. Non-uniform Speed
- When a body covers unequal distances in equal time intervals, it is said to be moving with non-uniform speed.
- Example: A car in city traffic where speed keeps changing.
3. Instantaneous Speed
- The speed of an object at a particular instant of time.
- Measured using: Speedometer in vehicles.
- Example: A car’s speed at a given moment while driving.
4. Average Speed
- The total distance travelled divided by total time taken.
- Formula: \begin{array}{l} v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \end{array}
- Example: A car covers 300 km in 5 hours. \begin{array}{l} v_{\text{avg}} = \frac{300}{5} = 60 \text{ km/h} \end{array}
Units of Speed
| System | Unit of Speed | Symbol |
|---|---|---|
| SI System | Metres per second | $m/s$ or $m s^{-1}$ |
| CGS System | Centimetres per second | $cm/s$ or $cm s^{-1}$ |
| Practical | Kilometres per hour | $km/h$ or $km h^{-1}$ |
Unit Conversions
- $1 m/s = 3.6 km/h$
- $1 km/h = \frac{5}{18} m/s$
Example
Convert 72 km/h into m/s: \begin{array}{l} 72 \times \frac{5}{18} = 20 \text{ m/s} \end{array}
Dimensional Formula of Speed
Since speed is defined as: \begin{array}{l} \text{Speed} = \frac{\text{Distance}}{\text{Time}} \end{array}
- Dimension of Distance = [$M^0L^1T^0$]
- Dimension of Time = [$M^0L^0T^1$]
Thus, \begin{array}{l} \text{Dimension of Speed} = [M^0L^1T^{-1}] \end{array}
Instruments to Measure Speed
- Speedometer
- Displays the instantaneous speed of a moving vehicle.
- Found in cars, bikes, and other vehicles.
- Reads speed in km/h.
- Odometer
- Measures the total distance travelled by a vehicle.
- Usually recorded in kilometres (km).
Graphical Representation of Speed
Distance-Time Graph for Uniform Speed
graph for a body having uniform
motion is a straight line.
- A straight line indicates constant speed.
- The slope of the graph gives the speed of the object.
Distance-Time Graph for Non-uniform Speed
for a body having non-uniform
motion is a curved line.
- A curved line indicates changing speed.
Concept of Relative Speed
- The speed of one object relative to another moving object.
- Formula:
- If two objects move in same direction: \begin{array}{l} v_{\text{relative}} = v_1 – v_2 \end{array}
- If two objects move in opposite directions: \begin{array}{l} v_{\text{relative}} = v_1 + v_2 \end{array}
Example
- A car moving at 60 km/h overtakes another moving at 40 km/h.
- Their relative speed: \begin{array}{l} v_{\text{relative}} = 60 – 40 = 20 \text{ km/h} \end{array}
Difference Between Speed and Velocity
| Property | Speed | Velocity |
|---|---|---|
| Definition | Distance covered per unit time | Displacement per unit time |
| Type | Scalar | Vector |
| Formula | $\begin{array}{l} \frac{\text{Distance}}{\text{Time}} \end{array}$ | $\begin{array}{l} \frac{\text{Displacement}}{\text{Time}} \end{array}$ |
| Direction | No direction | Has direction |
| Example | Car moving at 50 km/h | Car moving at 50 km/h towards east |
Real-Life Applications of Speed
- Road Transport: Speed limits help regulate traffic safety.
- Sports: Athletes measure speed to improve performance.
- Space Travel: Rockets travel at extremely high speeds.
- Aviation: Airplanes maintain speeds to ensure smooth flights.
Advanced Topics Related to Speed
1. Speed of Sound
- Speed of sound in air = $\begin{array}{l} 330 m/s \end{array}$
- Speed of sound in water = $\begin{array}{l} 1500 m/s \end{array}$
- Speed of sound in steel = $\begin{array}{l} 5000 m/s \end{array}$
2. Speed of Light
- Speed of light in vacuum: \begin{array}{l} c = 3.0 \times 10^8 \text{ m/s} \end{array}
Key Takeaways
✅ Speed is distance covered per unit time
✅ SI unit: $m/s$, Practical unit: $km/h$
✅ Speed is scalar, velocity is vector
✅ Instantaneous speed is measured using a speedometer
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