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Chapter 2: Problem 8

(II) A horse trots away from its trainer in a straight line, moving 38 m away in 9.0 s. It then turns abruptly and gallops halfway back in 1.8 s. Calculate (\(a\)) its average speed and (\(b\)) its average velocity for the entire trip, using "away from the trainer" as the positive direction.

Short Answer

Expert verified
Average speed: 5.28 m/s; average velocity: 1.76 m/s.

Step by step solution

01

Calculate Total Distance

The horse trots 38 m away and then gallops halfway back, which is \(\frac{38}{2} = 19\text{ m}\). The total distance traveled is the sum of these parts: \(38 + 19 = 57\text{ m}\).
02

Calculate Total Time

The time to trot away is 9.0 s and to gallop back is 1.8 s. Therefore, the total time taken is \(9.0 + 1.8 = 10.8\text{ s}\).
03

Calculate Average Speed

Average speed is total distance divided by total time. Using the values from Steps 1 and 2: \(\text{Average speed} = \frac{57\text{ m}}{10.8\text{ s}} \approx 5.28\text{ m/s}\).
04

Calculate Net Displacement

The net displacement is the final position relative to the initial position. The horse ends up 19 meters from the starting point in the positive direction.
05

Calculate Average Velocity

Average velocity is the net displacement divided by total time. Using 19 m from Step 4 and total time from Step 2: \(\text{Average velocity} = \frac{19\text{ m}}{10.8\text{ s}} \approx 1.76\text{ m/s}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance and Displacement
Understanding the difference between distance and displacement is crucial in kinematics. Distance refers to the total length of the path traveled irrespective of direction. It's always positive and gives us a scalar quantity.
For the exercise, the horse traveled away and back, covering a total distance of 57 m. Displacement, on the other hand, is a measure of the change in position. It's a vector quantity and can be positive, negative, or zero, depending on the direction relative to the starting point.
In our example, the horse's net displacement is 19 m. It represents the straight line from the starting point to the final position, showing a different magnitude than distance.
Kinematics
Kinematics is the branch of physics that describes motion without considering the forces causing it. It primarily focuses on quantities such as velocity, speed, distance, displacement, acceleration, and time.
Kinematics is fundamental for understanding motion because it breaks down complex movements into simple, descriptive traits. Often, problems involve calculating average speed and velocity, as they are essential metrics of motion.
  • Speed is a scalar quantity, having only magnitude. It is calculated by dividing the total distance by total time.
  • Velocity includes both magnitude and direction, making it a vector quantity. Average velocity is found by dividing displacement by total time.
Reading kinematic descriptions in a physics context is vital to analyze and predict the future behavior of moving objects.
Motion in a Straight Line
Motion in a straight line, often referred to as linear or rectilinear motion, is the simplest form of motion and forms the basis for understanding more complex motions.
In the provided exercise, the horse's motion is linear since it moves back and forth along a single path. This unidirectional motion simplifies calculations, only requiring us to track the changes along this one dimension. Understanding this motion includes analyzing the object's path, direction, and speed. Motion in a straight line concerns primarily linear displacement and linear direction. This simplicity allows us to easily compute variables like speed and velocity using basic arithmetic operations without extra geometry.

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Most popular questions from this chapter

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