5. An object moving in the x-y plane has a position vector given by: 7 = (2t³ - 5t)i + (6 - t^)ĵ (in meters). Find the particle's a. position vector at t = Os

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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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Only e, f, and g

### Problem Statement

**5.** An object moving in the x-y plane has a position vector given by: 

**\[ \vec{r} = (2t^3 - 5t)\hat{i} + (6 - t^4)\hat{j} \quad \text{(in meters)} \]**

Find the particle’s

**a. position vector at \( t = 0s \)**

**b. position vector at \( t = 2s \)**

**c. displacement vector for this change in position**

**d. average velocity during this motion**
Transcribed Image Text:### Problem Statement **5.** An object moving in the x-y plane has a position vector given by: **\[ \vec{r} = (2t^3 - 5t)\hat{i} + (6 - t^4)\hat{j} \quad \text{(in meters)} \]** Find the particle’s **a. position vector at \( t = 0s \)** **b. position vector at \( t = 2s \)** **c. displacement vector for this change in position** **d. average velocity during this motion**
### Physics Problem Set

**e. Velocity at \( t = 0 \)**

**f. Velocity at \( t = 2 \ \text{s} \) expressed as a magnitude and direction measured counterclockwise (CCW) from the x-axis**

**g. Acceleration at \( t = 2 \ \text{s} \) expressed as a magnitude and direction measured counterclockwise (CCW) from the x-axis**

For this section of your studies, you are required to determine the velocity and acceleration of a given object at specified instances and express these quantities with both magnitude and direction. Below are instructions on how to proceed:

1. **Velocity at \( t = 0 \):**
    - Determine the initial velocity of the object. This is the velocity at the start of the observation (i.e., at time \( t = 0 \)).

2. **Velocity at \( t = 2 \ \text{s} \):**
    - Calculate the velocity of the object at \( t = 2 \ \text{s} \).
    - Express the velocity as a magnitude.
    - Specify the direction of the velocity. This direction should be measured counterclockwise (CCW) from the x-axis.

3. **Acceleration at \( t = 2 \ \text{s} \):**
    - Calculate the acceleration of the object at \( t = 2 \ \text{s} \).
    - Express the acceleration as a magnitude.
    - Specify the direction of the acceleration. This direction should also be measured counterclockwise (CCW) from the x-axis.

Take note that understanding how to express both magnitude and direction is crucial for correctly interpreting vector quantities in physics. Make sure to use the appropriate mathematical tools and concepts to arrive at accurate results.
Transcribed Image Text:### Physics Problem Set **e. Velocity at \( t = 0 \)** **f. Velocity at \( t = 2 \ \text{s} \) expressed as a magnitude and direction measured counterclockwise (CCW) from the x-axis** **g. Acceleration at \( t = 2 \ \text{s} \) expressed as a magnitude and direction measured counterclockwise (CCW) from the x-axis** For this section of your studies, you are required to determine the velocity and acceleration of a given object at specified instances and express these quantities with both magnitude and direction. Below are instructions on how to proceed: 1. **Velocity at \( t = 0 \):** - Determine the initial velocity of the object. This is the velocity at the start of the observation (i.e., at time \( t = 0 \)). 2. **Velocity at \( t = 2 \ \text{s} \):** - Calculate the velocity of the object at \( t = 2 \ \text{s} \). - Express the velocity as a magnitude. - Specify the direction of the velocity. This direction should be measured counterclockwise (CCW) from the x-axis. 3. **Acceleration at \( t = 2 \ \text{s} \):** - Calculate the acceleration of the object at \( t = 2 \ \text{s} \). - Express the acceleration as a magnitude. - Specify the direction of the acceleration. This direction should also be measured counterclockwise (CCW) from the x-axis. Take note that understanding how to express both magnitude and direction is crucial for correctly interpreting vector quantities in physics. Make sure to use the appropriate mathematical tools and concepts to arrive at accurate results.
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