### Physics Problem: Force and Velocity**Problem Statement:**If the mass is initially at rest and the force is \( F = 3t^2 \) Newton where \( t \) is in seconds, what is the velocity of the mass at \( t = 6 \) s? There is no friction.**Diagram Explanation:**The diagram shows a block with a mass labeled as "4 kg" on a flat surface. An arrow labeled "F" is pointing to the right, indicating the direction of the applied force.**Options:**1. \( 54 \) m/s2. \( 216 \) m/s3. \( 9 \) m/s4. \( 162 \) m/s### Calculations:Given:- Mass \( m = 4 \) kg- Force \( F = 3t^2 \) Newton- Time \( t = 6 \) s- Initial velocity \( v_0 = 0 \) m/s (mass is initially at rest)1. **Newton's Second Law**: \( F = ma \) \[ a = \frac{F}{m} \] Substituting the given force, \[ a = \frac{3t^2}{4} \]2. **Acceleration**: \[ a(t) = \frac{3t^2}{4} \]3. **Velocity as a Function of Time**: Integrate the expression for acceleration: \[ v(t) = \int a(t) \, dt = \int \frac{3t^2}{4} \, dt = \frac{3}{4} \int t^2 \, dt = \frac{3}{4} \cdot \frac{t^3}{3} = \frac{t^3}{4} + C \] Since the initial velocity \( v_0 = 0 \) when \( t = 0 \), the constant \( C = 0 \), \[ v(t) = \frac{t^3}{4} \]4. **Velocity at \( t = 6 \) s**: \[ v(6) = \frac{6^3}{4} = \frac{216}{4} =

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Answered: If the mass is initially at rest and…

If the mass is initially at rest and the velocity of the mass at t = 6 s? There is no friction. 54 m/s 216 m/s 9 m/s O 162 m/s 4 kg F

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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