3. Use the vectors in the diagram below to answer the following questions. UB ü FD a) At one instant in time, a car has velocity vector A. After At = 1s, the car has a velocity vector g. Draw the average acceleration vector during this time span. b) Draw ür, if ₁ = ₁ + ₂ + c + p. (Try to maintain the relative lengths and directions of the vectors, but I recognize they will not be perfect. Show your work to prove you know what you're doing.) c) Determine the scalar component of c in the direction of p, given the following information. Show your work for full credit.

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Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Title: Vector Analysis in Physics**

**Instructions:**
Examine the vector diagrams and solve the following problems using vector analysis.

**Vector Diagram:**
Four vectors are displayed: \(\vec{v}_A\), \(\vec{v}_B\), \(\vec{v}_C\), and \(\vec{v}_D\).

**Problem 3:**

a) **Velocity Transition:**
   - A car initially moves with velocity vector \(\vec{v}_A\).
   - After a time interval \(\Delta t = 1 \text{s}\), the velocity changes to \(\vec{v}_B\).
   - **Task:** Illustrate the average acceleration vector for this transition.

b) **Vector Addition:**
   - **Task:** Depict \(\vec{v}_T\) such that \(\vec{v}_T = \vec{v}_A + \vec{v}_B + \vec{v}_C + \vec{v}_D\).
   - Notes: Attempt to keep the vector lengths and directions relatively accurate; precise scaling isn’t necessary.
   - Show calculations to validate your understanding.

c) **Scalar Component Calculation:**
   - **Objective:** Find the scalar component of \(\vec{v}_C\) in the direction of \(\vec{v}_D\).
   - Given Parameters:
     - Magnitude of \(\vec{v}_C\): \( |\vec{v}_C| = 6 \frac{\text{m}}{\text{s}} \)
     - Magnitude of \(\vec{v}_D\): \( |\vec{v}_D| = 5 \frac{\text{m}}{\text{s}} \)
     - Angle between \(\vec{v}_C\) and its vertical reference: \(50^\circ\)

Ensure that your calculations and illustrations are neat and logically structured.
Transcribed Image Text:**Title: Vector Analysis in Physics** **Instructions:** Examine the vector diagrams and solve the following problems using vector analysis. **Vector Diagram:** Four vectors are displayed: \(\vec{v}_A\), \(\vec{v}_B\), \(\vec{v}_C\), and \(\vec{v}_D\). **Problem 3:** a) **Velocity Transition:** - A car initially moves with velocity vector \(\vec{v}_A\). - After a time interval \(\Delta t = 1 \text{s}\), the velocity changes to \(\vec{v}_B\). - **Task:** Illustrate the average acceleration vector for this transition. b) **Vector Addition:** - **Task:** Depict \(\vec{v}_T\) such that \(\vec{v}_T = \vec{v}_A + \vec{v}_B + \vec{v}_C + \vec{v}_D\). - Notes: Attempt to keep the vector lengths and directions relatively accurate; precise scaling isn’t necessary. - Show calculations to validate your understanding. c) **Scalar Component Calculation:** - **Objective:** Find the scalar component of \(\vec{v}_C\) in the direction of \(\vec{v}_D\). - Given Parameters: - Magnitude of \(\vec{v}_C\): \( |\vec{v}_C| = 6 \frac{\text{m}}{\text{s}} \) - Magnitude of \(\vec{v}_D\): \( |\vec{v}_D| = 5 \frac{\text{m}}{\text{s}} \) - Angle between \(\vec{v}_C\) and its vertical reference: \(50^\circ\) Ensure that your calculations and illustrations are neat and logically structured.
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