### Part 2**Calculate the x- and y-components of the acceleration.**#### Answers:* αₓ = ![Information Icon](data:image/png) [ ] mm/s²* αᵧ = ![Information Icon](data:image/png) [ ] mm/s²---In this section, you will be provided with a task involving the calculation of the acceleration components along the x- and y-axes. You need to determine the values of αₓ and αᵧ which represent the acceleration in the x-direction and y-direction respectively. You are required to fill in these values in the provided fields.Additionally, there are information icons next to each input field. Clicking on these icons will provide you with helpful tips or information related to the task.Note: Ensure that the units of your answers are in millimeters per second squared (mm/s²). ### Problem DescriptionThe x- and y-motions of guides A and B, which have right-angle slots, control the curvilinear motion of the connecting pin P. This pin slides within both slots.For a short interval, the motions are governed by:\[ x = 12 + 0.55t^2 \]\[ y = 16 - 0.57t^3 \]where x and y are in millimeters, and t is in seconds. #### Tasks:1. Calculate the magnitudes of the velocity \( v \) and acceleration \( a \) of the pin for \( t = 2.5 \) seconds.2. Sketch the direction of the path and indicate its curvature for this instance.### Diagram DetailsA diagram illustrates the mechanical setup:- Two vertical and horizontal guides (A and B) control the pin P.- The guides are connected by the pin P, which slides within the horizontal and vertical slots.- The horizontal displacement \( x \) and the vertical displacement \( y \) are indicated and defined by the given equations. ### Solution Steps#### Part 1**Calculate the x- and y-components of the velocity.**\[ v_x = \frac{dx}{dt} = 2.75 \text{ mm/s} \]\[ v_y = \frac{dy}{dt} = -10.6785 \text{ mm/s} \]**Answers:**\[ v_x = 2.75 \text{ mm/s} \]\[ v_y = -10.6785 \text{ mm/s} \]### Visual Explanation- The diagram shows the mechanical setup of pin P sliding through guides A and B.- The x- and y-axes are clearly indicated, where displacement in the x-direction is governed by a quadratic equation and in the y-direction by a cubic equation.

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Calculate the x- and y-components of the acceleration. Answers: mm/s² ax mm/s² ay" i

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

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### Part 2

**Calculate the x- and y-components of the acceleration.**

#### Answers:
* αₓ = ![Information Icon](data:image/png) [ ] mm/s²
* αᵧ = ![Information Icon](data:image/png) [ ] mm/s²

---

In this section, you will be provided with a task involving the calculation of the acceleration components along the x- and y-axes. You need to determine the values of αₓ and αᵧ which represent the acceleration in the x-direction and y-direction respectively. You are required to fill in these values in the provided fields.

Additionally, there are information icons next to each input field. Clicking on these icons will provide you with helpful tips or information related to the task.

Note: Ensure that the units of your answers are in millimeters per second squared (mm/s²).

### Problem Description

The x- and y-motions of guides A and B, which have right-angle slots, control the curvilinear motion of the connecting pin P. This pin slides within both slots.

For a short interval, the motions are governed by:
\[ x = 12 + 0.55t^2 \]
\[ y = 16 - 0.57t^3 \]

where x and y are in millimeters, and t is in seconds.

#### Tasks:
1. Calculate the magnitudes of the velocity \( v \) and acceleration \( a \) of the pin for \( t = 2.5 \) seconds.
2. Sketch the direction of the path and indicate its curvature for this instance.

### Diagram Details

A diagram illustrates the mechanical setup:
- Two vertical and horizontal guides (A and B) control the pin P.
- The guides are connected by the pin P, which slides within the horizontal and vertical slots.
- The horizontal displacement \( x \) and the vertical displacement \( y \) are indicated and defined by the given equations.

### Solution Steps

#### Part 1
**Calculate the x- and y-components of the velocity.**

\[ v_x = \frac{dx}{dt} = 2.75 \text{ mm/s} \]
\[ v_y = \frac{dy}{dt} = -10.6785 \text{ mm/s} \]

**Answers:**

\[ v_x = 2.75 \text{ mm/s} \]
\[ v_y = -10.6785 \text{ mm/s} \]

### Visual Explanation

- The diagram shows the mechanical setup of pin P sliding through guides A and B.
- The x- and y-axes are clearly indicated, where displacement in the x-direction is governed by a quadratic equation and in the y-direction by a cubic equation.

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