2.3.1 Speed

In our daily lives, we often talk about how fast things are moving. We might say a car is "fast" or a snail is "slow." In physics, we need a more precise way to describe this. The concept of speed allows us to quantify how fast an object is moving by relating the distance it covers to the time it takes. Understanding speed is fundamental to the study of motion.

Definition

Speed is the measure of the distance covered by an object with the passage of time. It tells us the rate at which an object is moving. It is a scalar quantity, meaning it has magnitude (size) but no direction.

Mathematically: speed = distanceelapsed time or v = Δ dΔ t

Main Idea

The main idea is that speed quantifies how fast an object is moving. To determine speed, you need two pieces of information: the distance the object has traveled and the time it took to travel that distance. A fast-moving object covers a large distance in a short time, resulting in a high speed. A slow-moving object covers a small distance in a given time, resulting in a low speed. Speed is a scalar, so it does not matter in which direction the object moved.

Core Concept

• The distance traveled by the object.
• The time that has elapsed while covering this distance.

Formula and Units The formula for speed is: v = Δ dΔ t where: - v is the speed. - Δ d is the distance covered. - Δ t is the elapsed time.

The SI unit of speed is metre per second (m/s or m·s^-1). Another common unit is kilometre per hour (km/h).

The speed will be one metre per second if an object covers one metre of distance in one second.

Example from Text The text provides a real-world example: while going from Islamabad to Peshawar through motorway M1, we leave at Tarnol interchange at 2:00 pm and cross Sawabi interchange at 3:00 pm. Since Sawabi interchange is about 70 km from Tarnol interchange and it took us one hour, our speed can be obtained as: v = 70 km1 hr = 70 km/hr

• A fast-moving object covers a relatively large distance in a given amount of time and thus has a high speed.
• A slow-moving object covers a relatively small amount of distance in the same amount of time and therefore has a low speed.

Detailed Explanation

Speed is a fundamental concept in kinematics. It describes the rate of motion without any concern for the direction of that motion. This makes it a scalar quantity.

• For a given time, the greater the distance, the greater the speed.
• For a given distance, the shorter the time, the greater the speed.

This is why a car that travels 100 km in 1 hour (100 km/h) is faster than a car that travels 100 km in 2 hours (50 km/h).

The Nature of Speed Because speed is a scalar, it only has magnitude. It is always a positive number (or zero). It does not have a direction associated with it. For example, if you are driving at 60 km/h, your speed is 60 km/h, regardless of whether you are driving North, South, East, or West.

• Fastest man on Earth: Usain Bolt finished a 100-metre sprint in just 9.58 seconds in 2009. His speed was 10.44 m/s or 37.58 km/h.
• Slowest animal: The three-toed sloth has an average speed of about 0.00134112 m/s or 0.0048 km/h.
• Fastest animal in the world: The Peregrine Falcon can attain a maximum speed of up to 108.333 m/s or 390 km/h.
• Fastest land animal: The Cheetah can reach a speed of 33.33 m/s or 120 km/h.

Intermediate Level

Speed is a scalar quantity, which means it does not have a direction. It is a measure of the rate of change of distance. In physics problems, you often need to calculate average speed for a journey. Average speed is the total distance traveled divided by the total time taken. It is different from instantaneous speed, which is the speed at a specific moment in time (like what a car's speedometer shows). The distinction between speed and velocity becomes crucial when the direction of motion changes. For example, a car moving at a constant speed around a circular track has a constant speed, but its velocity is continuously changing because its direction is changing. This is why understanding speed as a scalar is essential before moving on to vector quantities.

Important Points

• - Speed is the rate of change of distance.
• - It is a scalar quantity (magnitude only, no direction).
• - The formula for speed is v = dt.
• - The SI unit of speed is metre per second (m/s).
• - Speed tells us how fast an object is moving.
• - A fast object covers a large distance in a short time.

Remember

• - Speed = Distance / Time.
• - Speed is a scalar. No direction.
• - SI unit: m/s.
• - Fast object: High speed (large distance in short time).
• - Slow object: Low speed (small distance in long time).

Common Mistakes

• - Confusing speed with velocity: Speed is a scalar, velocity is a vector. They are not the same.
• - Forgetting the unit: A speed value must have a unit (e.g., 60 km/h), not just a number (e.g., 60).
• - Using the wrong units: Make sure the distance and time units are consistent. If distance is in km and time is in hours, the speed will be in km/h. If you need m/s, you must convert the units.

Quick Revision

Speed is a scalar quantity that measures how fast an object is moving. It is calculated as the distance covered divided by the time taken (v = dt). The SI unit of speed is metre per second (m/s). Speed only has magnitude and no direction, meaning it does not matter in which direction the object is moving.

60-Second Revision

• Formula: Speed = Distance / Time.
• Scalar: No direction.
• Unit: m/s.
• **Example:** 70 km in 1 hour = 70 km/h.
• Fast object: Large distance in short time.

Frequently Asked Questions (FAQs)

• Q1. What is speed?
• Answer: Speed is the measure of how fast an object is moving. It is the distance covered by an object per unit time.

• Q2. What is the formula for speed?
• Answer: The formula for speed is:
• Speed = DistanceTime
• or v = Δ dΔ t.

• Q3. What is the SI unit of speed?
• Answer: The SI unit of speed is metre per second (m/s or m·s^-1).

• Q4. Is speed a scalar or a vector quantity?
• Answer: Speed is a scalar quantity. It has magnitude but no direction.

Q5. How is speed different from velocity? Answer: Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). Speed tells you how fast an object is moving, while velocity tells you how fast and in which direction.

Q6. What is the difference between average speed and instantaneous speed? Answer: Average speed is the total distance traveled divided by the total time taken. Instantaneous speed is the speed of an object at a specific instant in time (like a speedometer reading).

• Q7. If a car travels 120 km in 2 hours, what is its average speed?
• Answer: Average speed = Total distance / Total time = 120 km / 2 h = 60 km/h.

Multiple Choice Questions (MCQs)

• Q1. Speed is defined as:
• A. Distance multiplied by time
• B. Distance divided by time
• C. Time divided by distance
• D. Displacement divided by time

• Correct Answer: B
• Explanation: The text defines speed as the measure of the distance covered with the passage of time, or v = dt.

• Q2. Speed is a:
• A. Vector quantity
• B. Scalar quantity
• C. Base quantity
• D. Derived quantity

• Correct Answer: B
• Explanation: Speed is a scalar quantity because it has magnitude but no direction.

• Q3. The SI unit of speed is:
• A. Metre (m)
• B. Second (s)
• C. Metre per second (m/s)
• D. Newton (N)

• Correct Answer: C
• Explanation: The text states that the SI unit of speed is metre per second (m/s).

• Q4. If an object covers 70 km in 1 hour, its speed is:
• A. 70 km/h
• B. 70 m/s
• C. 35 km/h
• D. 140 km/h

• Correct Answer: A
• Explanation: The text uses this example to calculate speed as 70 km / 1 hr = 70 km/hr.

• Q5. An object is considered to have a high speed if it:
• A. Covers a small distance in a long time
• B. Covers a large distance in a short time
• C. Does not move at all
• D. Moves in a circle

• Correct Answer: B
• Explanation: The text states that a fast-moving object covers a relatively large distance in a given amount of time and thus has a high speed.

• Q6. Which of the following is NOT a unit of speed?
• A. m/s
• B. km/h
• C. miles per hour
• D. Newton

• Correct Answer: D
• Explanation: Newton is a unit of force, not speed. m/s, km/h, and miles per hour are all units of speed.

• Q7. Usain Bolt's speed during his 100-metre sprint was approximately:
• A. 10 m/s
• B. 100 m/s
• C. 1 m/s
• D. 0.1 m/s

• Correct Answer: A
• Explanation: The text states that his speed was 10.44 m/s (approximately 10 m/s).

• Q8. The slowest animal mentioned in the text is the:
• A. Cheetah
• B. Peregrine Falcon
• C. Three-toed sloth
• D. Garden snail

• Correct Answer: C
• Explanation: The text states that the slowest animal in the world is the three-toed sloth.

• Q9. Which of the following is true about speed?
• A. It has both magnitude and direction.
• B. It is always negative.
• C. It is a scalar quantity.
• D. It is measured in newtons.

• Correct Answer: C
• Explanation: Speed is a scalar quantity, meaning it has magnitude only.

• Q10. If a car travels at a constant speed of 60 km/h, it covers:
• A. 60 km every minute
• B. 60 km every hour
• C. 60 m every second
• D. 60 km every second

• Correct Answer: B
• Explanation: A speed of 60 km/h means the car covers 60 kilometres in one hour.

Frequently Asked Questions (FAQs)

Q1. What is the difference between speed and average speed? Answer: Speed is a general term for how fast an object is moving. Average speed is the total distance traveled divided by the total time taken for a journey. Average speed is used when the speed of an object varies over time.

• Q2. What is instantaneous speed?
• Answer: Instantaneous speed is the speed of an object at a specific moment in time. It is the reading you would see on a car's speedometer at any given instant.

• Q3. Can speed be zero?
• Answer: Yes. If an object is at rest, its speed is zero. This means it is not covering any distance over time.

Q4. How is speed related to distance and time? Answer: Speed is directly proportional to distance (for a given time) and inversely proportional to time (for a given distance). This means that for the same time, a larger distance gives a higher speed, and for the same distance, a longer time gives a lower speed.

Q5. What is the speed of light? Answer: The speed of light in a vacuum is approximately 3 × 10⁸ m/s. This is a fundamental constant in physics and is the universal speed limit.

Q6. Why do we use different units for speed like km/h and m/s? Answer: Different units are convenient for different situations. km/h is more intuitive for everyday speeds like cars. m/s is the SI unit and is used in most scientific calculations. You can convert between them: 1 km/h = 1000 m3600 s = 518 m/s ≈ 0.278 m/s.

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