### Robot Arm Motion AnalysisFor a short time, the arm of the robot is extending at a constant rate such that \( \dot{r} = 1.5 \, \text{ft/s} \) when \( r = 3 \, \text{ft} \). The position functions are given as \( z = \left(4t^2\right) \, \text{ft} \) and \( \theta = 0.5t \, \text{rad} \), where \( t \) is in seconds.---### Problem Statement:**Part A:** Determine the magnitude of the velocity of the grip A when \( t = 3 \, \text{s} \). Express your answer to three significant figures and include the appropriate units.**\( v = \) [Input Box]****Part B:**Determine the magnitude of the acceleration of the grip A when \( t = 3 \, \text{s} \). Express your answer to three significant figures and include the appropriate units.**\( a = \) [Input Box]**---### Explanation of Diagram:The diagram provided on the right side of the screen shows the robotic arm, which is extending outward along the \( r \)-axis. The grip, labeled as point A, is located at the end of the arm. - The cylindrical base of the robot is fixed.- The arm, represented in yellow, extends linearly in the radial direction, \( r \).- The grip A is shown moving along a path described by the functions \( z \) (vertical displacement) and \( \theta \) (angular displacement).---Please provide your answers in the input boxes corresponding to Part A and Part B.---This exercise aims at applying kinematic equations to analyze the motion of a robotic arm in three-dimensional space, taking into consideration radial, vertical, and angular movements.

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For a short time the arm of the robot is etending at a constant rate such that i- 1.5 ft/s when r- 3 ft, z= (4) ft, and 0 = 0.5t rad, where tis in seconds. Part A Determine the magnitude of the velocity of the grip A when t= 38. Express your answer to three significant figures and include the appropriate units. Part B Determine the magnitude of the acceleration of the grip A when t= 3s. Express your answer to three significant figures and include the appropriate units.

For a short time the arm of the robot is etending at a constant rate such that i- 1.5 ft/s when r- 3 ft, z= (4) ft, and 0 = 0.5t rad, where tis in seconds. Part A Determine the magnitude of the velocity of the grip A when t= 38. Express your answer to three significant figures and include the appropriate units. Part B Determine the magnitude of the acceleration of the grip A when t= 3s. Express your answer to three significant figures and include the appropriate units.

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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Question

### Robot Arm Motion Analysis

For a short time, the arm of the robot is extending at a constant rate such that \( \dot{r} = 1.5 \, \text{ft/s} \) when \( r = 3 \, \text{ft} \). The position functions are given as \( z = \left(4t^2\right) \, \text{ft} \) and \( \theta = 0.5t \, \text{rad} \), where \( t \) is in seconds.

---

### Problem Statement:

**Part A:**
Determine the magnitude of the velocity of the grip A when \( t = 3 \, \text{s} \).
Express your answer to three significant figures and include the appropriate units.

**\( v = \) [Input Box]**

**Part B:**
Determine the magnitude of the acceleration of the grip A when \( t = 3 \, \text{s} \).
Express your answer to three significant figures and include the appropriate units.

**\( a = \) [Input Box]**

---

### Explanation of Diagram:
The diagram provided on the right side of the screen shows the robotic arm, which is extending outward along the \( r \)-axis. The grip, labeled as point A, is located at the end of the arm.

- The cylindrical base of the robot is fixed.
- The arm, represented in yellow, extends linearly in the radial direction, \( r \).
- The grip A is shown moving along a path described by the functions \( z \) (vertical displacement) and \( \theta \) (angular displacement).

---

Please provide your answers in the input boxes corresponding to Part A and Part B.

---

This exercise aims at applying kinematic equations to analyze the motion of a robotic arm in three-dimensional space, taking into consideration radial, vertical, and angular movements.

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