### Learning Goal:A particle of mass \( M \) moves along a straight line with initial speed \( v_1 \). A force of magnitude \( F \) pushes the particle a distance \( s \) along the direction of its motion.---This goal focuses on understanding the motion of a particle under the influence of a force. By analyzing these parameters, students can learn about fundamental principles in physics, such as Newton's laws of motion, work, energy, and kinematics. The key elements of this problem are:1. **Mass of the Particle (\( M \))**: Provides a measure of the amount of matter in the particle, which is a basic property influencing its motion when a force is applied.2. **Initial Speed (\( v_1 \))**: This is the velocity of the particle at the start of its motion.3. **Applied Force (\( F \))**: The magnitude of the external force applied to the particle. This force will change the particle's velocity and subsequently its kinetic energy and position over time.4. **Distance (\( s \))**: The distance over which the force is applied in the direction of the particle's motion.By solving such problems, students develop a better understanding of dynamic systems and the application of physical laws to predict future states of motion. Visual aids, such as diagrams showing the direction of the force and the trajectory of the particle, can greatly enhance comprehension. For instance, a graph plotting the particle’s velocity or position over time under these conditions could provide significant insight into the particle's behavior. ### Part A**Find \( v_f \), the particle’s final speed after the particle has traveled a distance \( s \).****Express your answer in terms of \( v_i \), \( M \), \( F \), and \( s \).** View Available Hint(s) The formula provided in the answer box is:\[ v_f = \sqrt{v_i^2 + \frac{2FD}{M}} \]**Explanation of Variables:**- \( v_f \): Final speed of the particle- \( v_i \): Initial speed of the particle- \( M \): Mass of the particle- \( F \): Force applied to the particle- \( D \): Distance traveled by the particle**Instructions:**Input the derived formula into the answer box and click the "Submit" button to check your answer.**Notes:**- After submission, if the answer is incorrect, a message will appear indicating the number of attempts remaining.**Example Calculation:**For instance, if \( v_i = 5 \, \text{m/s} \), \( M = 10 \, \text{kg} \), \( F = 20 \, \text{N} \), and \( D = 15 \, \text{m} \), then:\[ v_f = \sqrt{5^2 + \frac{2 \times 20 \times 15}{10}} \]\[ v_f = \sqrt{25 + 60} \]\[ v_f = \sqrt{85} \]\[ v_f \approx 9.22 \, \text{m/s} \]A red "X" icon indicates an incorrect submission with a note to try again and mentions that there are 5 attempts remaining.

To find: The final speed of the particle. Given: The initial speed is vi. The mass of the particle…

Answered: Learning Goal: A particle of mass M…

Learning Goal: A particle of mass M moves along a straight line with initial speed v₁. A force of magnitude F pushes the particle a distance s along the direction of its motion.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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