Measuring the Rate of Motion

Speed

• Definition: Speed is the distance traveled by an object in unit time.
• Units: The SI unit of speed is metre per second (m/s). Other units include centimetres per second (cm/s) and kilometres per hour (km/h).
• Characteristics:
  • Speed is a scalar quantity, meaning it has only magnitude and no direction.
  • It can vary; an object's speed need not be constant.
  • Average speed is calculated using the formula:

$$\text{Average speed} = \frac{\text{Total distance travelled}}{\text{Total time taken}}$$

Examples:

1. A car travels 100 km in 2 hours. Its average speed is 50 km/h.
2. A bicycle covers 30 km in 1.5 hours, resulting in an average speed of 20 km/h.
3. A runner completes a 400 m track in 50 seconds, giving an average speed of 8 m/s.

Questions:

1. Q: What is the formula to calculate average speed?
   • A: Average speed = Total distance travelled / Total time taken.
2. Q: What are the units of speed?
   • A: The SI unit is m/s; other units include cm/s and km/h.
3. Q: Can speed remain constant during travel?
   • A: No, speed can vary; average speed is used when speed changes.
4. Q: What does an average speed of 50 km/h indicate?
   • A: It indicates that the object travels 50 km in one hour.
5. Q: Is speed a vector or scalar quantity?
   • A: Speed is a scalar quantity as it has only magnitude.

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Velocity

• Definition: Velocity is the speed of an object in a specific direction.
• Characteristics:
  • Velocity can be uniform (constant speed and direction) or variable (changing speed/direction).
  • Average velocity is calculated using the formula:

$$\text{Average velocity} = \frac{\text{Initial velocity} + \text{Final velocity}}{2}$$

Examples:

1. A car accelerates from 30 m/s to 70 m/s over a period of time, resulting in an average velocity of 50 m/s.
2. A cyclist travels east at 15 m/s. Here, the velocity is 15 m/s east.
3. An object moving in a straight line and returning to the starting point has an average velocity of 0 m/s.

Questions:

1. Q: How is velocity different from speed?
   • A: Velocity includes direction; speed does not.
2. Q: What formula is used to calculate average velocity?
   • A: Average velocity = (Initial velocity + Final velocity) / 2.
3. Q: Can velocity change while speed remains constant?
   • A: Yes, if the direction changes while speed stays the same.
4. Q: If a car travels 100 m east in 10 seconds, what is its velocity?
   • A: Its velocity is 10 m/s east.
5. Q: What does an average velocity of 0 m/s signify?
   • A: It signifies that the object returned to its starting point.

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Comparison of Velocity and Speed

Aspect	Speed	Velocity
Definition	The distance traveled per unit of time, regardless of direction.	The rate of change of displacement in a specific direction.
Magnitude	Scalar quantity (only magnitude).	Vector quantity (magnitude + direction).
Direction	Does not have a direction.	Has a specific direction.
Formula	Speed = Distance / Time	Velocity = Displacement / Time
Unit	SI unit is meters per second (m/s).	SI unit is also meters per second (m/s).
Change	A change in speed does not affect its direction.	A change in velocity involves a change in either speed, direction, or both.
Example	A car moving at 60 km/h.	A car moving 60 km/h north.
Graphical Representation	Represented as a straight line with no direction in distance-time graph.	Represented as a straight line with a slope showing direction in a displacement-time graph.
Nature	Scalar (only magnitude, no direction).	Vector (magnitude and direction).
Use	Describes how fast an object is moving.	Describes how fast and in which direction an object is moving.

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Scenario-Based Questions

1. Scenario: You ride your bike from your house to school at a speed of 12 km/h.

   • Question: How would you express this situation in terms of velocity?
   • Answer: My velocity is 12 km/h in the direction of my school.

2. Scenario: You notice a car moving slower than you on the highway.

   • Question: What could be the implications for your average speed versus average velocity?
   • Answer: My average speed may be higher, but the car's velocity might be affected by traffic or direction changes.

3. Scenario: You run 500 meters and then walk back the same distance.

   • Question: What can you say about your average velocity?
   • Answer: Your average velocity is 0 m/s because the displacement is zero.

4. Scenario: You are timing your friend’s run on a 200 m track.

   • Question: If he completes it in 30 seconds, what is his average speed?
   • Answer: His average speed is $\frac{200 \text{ m}}{30 \text{ s}} \approx 6.67 \text{ m/s}$.

5. Scenario: You watch a plane flying at a constant speed on a straight path.

   • Question: What can be inferred about its velocity?
   • Answer: The plane has a uniform velocity, as both speed and direction are constant.

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