Rate of Change of Velocity

Key Points

1. Definition of Velocity and Its Change

• Uniform Motion: When an object moves at a constant velocity, its speed does not change over time. Hence, the change in velocity is zero.
• Non-Uniform Motion: Here, the velocity varies at different instances. This means the object's speed is changing, leading to a non-zero change in velocity.

Examples:

• A car moving at a steady speed of 50 km/h is in uniform motion.
• A bicycle accelerating from rest to 20 km/h over a distance is in non-uniform motion.

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2. Introducing Acceleration

• Acceleration: It is defined as the rate of change of velocity per unit time. It tells us how quickly the velocity of an object is changing.

• Formula for acceleration:

  $$\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}}$$

Examples:

• If a car's velocity increases from 20 m/s to 40 m/s in 5 seconds, the acceleration is $\frac{20 \text{ m/s}}{5 \text{ s}} = 4 \text{ m/s}²$.
• For an athlete speeding up from a jog (5 m/s to 15 m/s) in 10 seconds, the acceleration is $\frac{10 \text{ m/s}}{10 \text{ s}} = 1 \text{ m/s}²$.

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3. Types of Acceleration

• Positive Acceleration: When the acceleration is in the direction of the velocity. For example, when a car speeds up.
• Negative Acceleration (Deceleration): When acceleration acts against the direction of velocity, like when a vehicle slows down.

Examples:

• A rocket launching upward shows positive acceleration.
• A cyclist applying brakes exhibits negative acceleration.

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4. Uniform and Non-Uniform Acceleration

• Uniform Acceleration: Occurs when the change in velocity is consistent over equal time intervals, e.g., a freely falling object.
• Non-Uniform Acceleration: The change in velocity varies over equal time intervals, e.g., a car that speeds up and slows down unpredictably.

Examples:

• A freely falling apple accelerates uniformly at $9.8 m/s²$.
• A car racing with inconsistent speed changes has non-uniform acceleration.

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Questions and Answers

1. Q: When is a body said to be in uniform acceleration?
   • A: When its velocity changes by equal amounts in equal intervals of time.
2. Q: What do we mean by non-uniform acceleration?
   • A: It refers to an object's velocity changing by unequal amounts in equal intervals of time.
3. Q: How is acceleration calculated?
   • A: By the formula $a = \frac{v - u}{t}$, where $v$ is final velocity, $u$ is initial velocity, and $t$ is time.
4. Q: What unit is acceleration measured in?
   • A: The SI unit of acceleration is $m/s²$.
5. Q: Give an example of uniform acceleration in real life.
   • A: A car accelerating steadily from a stoplight with the same rate of increase in speed.

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Scenario-Based Questions

1. Scenario: You are playing basketball and sprinting towards the basket.

   • Question: How does your acceleration likely change while running?
   • Answer: My acceleration increases as I sprint faster towards the basket.

2. Scenario: You are on a roller coaster going downhill.

   • Question: What type of acceleration are you experiencing?
   • Answer: I am experiencing positive acceleration as the coaster speeds up going down.

3. Scenario: You are driving a car and approaching a red traffic light.

   • Question: What action will cause negative acceleration?
   • Answer: Pressing the brakes will cause negative acceleration as I slow down.

4. Scenario: You observe a train starting its journey.

   • Question: What type of acceleration does the train show at the start?
   • Answer: The train exhibits uniform acceleration if it increases its speed consistently.

5. Scenario: While riding a bike, you go downhill and then hit a flat road where you start pedaling faster.

   • Question: What type of acceleration occurs when you increase your pedaling speed?
   • Answer: This is an example of positive acceleration as my speed increases.

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