Section 11.2 Speed And Velocity Answer Key

Section 11.2: Speed and Velocity – A Comprehensive Guide with Answers

Understanding speed and velocity is fundamental to grasping the concepts of motion in physics. This comprehensive guide delves into Section 11.2, typically covering the definitions, calculations, and distinctions between these two crucial concepts. We'll explore various problem-solving approaches and provide detailed answers to common questions, ensuring a thorough understanding of this important physics section. Remember, this guide is designed to help you learn; it's crucial to attempt the problems yourself before reviewing the solutions.

What is Speed?

Speed, in its simplest form, measures how quickly an object is moving. It's a scalar quantity, meaning it only has magnitude (size) and no direction. We express speed as the distance covered divided by the time taken.

Formula:

• Speed = Distance / Time

The units of speed commonly used are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Example: If a car travels 100 kilometers in 2 hours, its average speed is 50 km/h (100 km / 2 hours = 50 km/h).

Types of Speed:

• Average Speed: The total distance traveled divided by the total time taken. This doesn't account for variations in speed during the journey.
• Instantaneous Speed: The speed of an object at a specific moment in time. Think of the speedometer in a car – it shows instantaneous speed.

What is Velocity?

Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. It describes the rate of change of an object's position. A change in either speed or direction results in a change in velocity.

Formula:

• Velocity = Displacement / Time

Displacement is the shortest distance between the starting and ending points, taking direction into account. Unlike distance, displacement is not the total path length.

Units: Velocity uses the same units as speed (m/s, km/h, mph), but it also includes a direction (e.g., 50 km/h north).

Example: If a car travels 100 kilometers east in 2 hours, its average velocity is 50 km/h east. If the car then travels 50 kilometers west in 1 hour, its average velocity for the entire journey changes, considering the net displacement.

Key Differences between Speed and Velocity:

Problem Solving Strategies and Answers (Illustrative Examples):

Let's tackle some sample problems to solidify your understanding. Remember to always identify the knowns, unknowns, and the appropriate formula before starting the calculation.

Problem 1: A cyclist travels 20 km in 1 hour, then rests for 30 minutes, and finally travels another 10 km in 30 minutes. Calculate the cyclist's:

(a) Average speed for the entire journey.

(b) Average velocity if the cyclist travels in a straight line.

Solution:

(a) Average Speed:

1. Total distance: 20 km + 10 km = 30 km
2. Total time: 1 hour + 0.5 hours + 0.5 hours = 2 hours
3. Average speed: 30 km / 2 hours = 15 km/h

(b) Average Velocity:

Since the cyclist travels in a straight line, the displacement is the total distance covered (30 km).

1. Total displacement: 30 km
2. Total time: 2 hours
3. Average velocity: 30 km / 2 hours = 15 km/h (in the direction of travel)

Problem 2: A car accelerates from rest to 60 m/s in 10 seconds. What is its acceleration?

Solution:

This problem involves acceleration, which is the rate of change of velocity.

1. Initial velocity (u): 0 m/s (rest)
2. Final velocity (v): 60 m/s
3. Time (t): 10 s
4. Formula for acceleration (a): a = (v - u) / t
5. Acceleration: a = (60 m/s - 0 m/s) / 10 s = 6 m/s²

Problem 3: A ball is thrown vertically upward with an initial velocity of 20 m/s. Neglecting air resistance, what is its velocity after 2 seconds? (Assume g = 10 m/s²)

Solution:

This involves understanding the effect of gravity on vertical motion. Gravity causes a downward acceleration of approximately 10 m/s².

1. Initial velocity (u): 20 m/s (upward, positive)
2. Acceleration (a): -10 m/s² (downward, negative)
3. Time (t): 2 s
4. Formula: v = u + at
5. Final velocity (v): v = 20 m/s + (-10 m/s²)(2 s) = 0 m/s

Problem 4: A bird flies 100 meters north, then 50 meters east, and finally 20 meters south. Calculate the bird's:

(a) Total distance traveled

(b) Displacement

Solution:

(a) Total distance: 100 m + 50 m + 20 m = 170 m

(b) Displacement: We need to use vector addition. Think of this as a right-angled triangle. The northward displacement is 80 meters (100 m - 20 m). The eastward displacement is 50 meters. The magnitude of the displacement is the hypotenuse:

• √(80² + 50²) ≈ 94.3 meters. The direction would be calculated using trigonometry (arctan(50/80) to find the angle relative to the north direction).

Advanced Concepts and Applications:

Section 11.2 may also introduce concepts like:

• Relative Velocity: The velocity of an object relative to another object. For example, the speed of a train relative to a stationary observer on the ground versus the speed of the train relative to a person on another moving train.
• Graphical Representation of Motion: Using graphs (displacement-time graphs, velocity-time graphs) to analyze motion, determine speed, velocity, and acceleration.
• Vectors and Vector Addition: Essential for understanding velocity and other vector quantities.

Conclusion:

Mastering Section 11.2 requires a solid understanding of the definitions of speed and velocity, their differences, and the ability to apply the relevant formulas to solve problems. This comprehensive guide, with its illustrative examples and explanations, aims to provide a robust foundation in these fundamental concepts. Remember to practice consistently; the more problems you solve, the stronger your understanding will become. By understanding the distinction between scalar and vector quantities, you’ll be well-equipped to tackle more complex physics problems in the future. This detailed exploration goes beyond a simple answer key, offering a pathway to truly understanding the underlying principles of motion.