### Problem DescriptionA model car is moving on a circular track of radius \( r = 2.8 \, \text{m} \), with the angle \( \Theta \) (in degrees) given by the formula:\[ \Theta = \Theta(t) = 60t - t^2 \]where \( t \) is in seconds.### TaskFind, at \( t = 1.5 \, \text{s} \):(a) The car's position (i.e., the angle \( \Theta \)); draw an accurate diagram showing the car in this position.(b) The car's velocity (magnitude and direction).(c) The car's acceleration (magnitude and direction).**Keep in mind that many of the formulas we’ve discussed require \( \Theta \) to be measured in radians.**### Diagram ExplanationThe diagram features a circular path with a radius \( r \). A radial arrow indicates the position of the car on the path, labeled with the angle \( \Theta \). The equation to calculate \( \Theta \) is provided, and it's marked that \( r = 2.8 \, \text{m} \) and \( \Theta \) is defined in degrees, emphasizing the necessity to convert to radians when using certain formulas.

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A model car is moving on a circular track of radius r = 208m₁ (in degrees) given by the formula shown above. with the angle Find, at t= 1.55= (a) the car's position (ie, the angle 0); draw an accurate diagram Showing the car in this position (b) the car's velocity (meg and direc) (c) the car's acceleration (mag and direc) Keep in mind that measured in radians. many of the formulas we've discussed require I to be

A model car is moving on a circular track of radius r = 208m₁ (in degrees) given by the formula shown above. with the angle Find, at t= 1.55= (a) the car's position (ie, the angle 0); draw an accurate diagram Showing the car in this position (b) the car's velocity (meg and direc) (c) the car's acceleration (mag and direc) Keep in mind that measured in radians. many of the formulas we've discussed require I to be

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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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

### Problem Description

A model car is moving on a circular track of radius \( r = 2.8 \, \text{m} \), with the angle \( \Theta \) (in degrees) given by the formula:

\[ \Theta = \Theta(t) = 60t - t^2 \]

where \( t \) is in seconds.

### Task

Find, at \( t = 1.5 \, \text{s} \):

(a) The car's position (i.e., the angle \( \Theta \)); draw an accurate diagram showing the car in this position.

(b) The car's velocity (magnitude and direction).

(c) The car's acceleration (magnitude and direction).

**Keep in mind that many of the formulas we’ve discussed require \( \Theta \) to be measured in radians.**

### Diagram Explanation

The diagram features a circular path with a radius \( r \). A radial arrow indicates the position of the car on the path, labeled with the angle \( \Theta \). The equation to calculate \( \Theta \) is provided, and it's marked that \( r = 2.8 \, \text{m} \) and \( \Theta \) is defined in degrees, emphasizing the necessity to convert to radians when using certain formulas.

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