**Educational Content: Understanding Average Velocity**---**Problem Statement:**The positions of a particle at times \( t = 1, 2, \) and \( 3 \) are given below. What is the average velocity of the particle in the time interval \([1, 3]\)?- \( r(1) = \langle 2, 0, 3 \rangle \)- \( r(2) = \langle 1, 1, 1 \rangle \)- \( r(3) = \langle -2, 4, 1 \rangle \)**Select one:**- a. 5- b. \( \langle 1, 1, 1 \rangle \)- c. 3- d. \( \langle -2, 2, -1 \rangle \)- e. \( \langle -1, 3, 1 \rangle \)---**Solution Explanation:**1. **Understanding Vectors:** - Each \( r(t) \) represents the position of a particle in three-dimensional space at a given time \( t \).2. **Average Velocity Calculation:** - Average velocity is defined as the change in position divided by the change in time. - Calculate the change in position: \[ \Delta r = r(3) - r(1) = \langle -2, 4, 1 \rangle - \langle 2, 0, 3 \rangle = \langle -4, 4, -2 \rangle \] - Calculate the change in time: \[ \Delta t = 3 - 1 = 2 \] - Compute the average velocity: \[ \text{Average Velocity} = \frac{\Delta r}{\Delta t} = \left\langle \frac{-4}{2}, \frac{4}{2}, \frac{-2}{2} \right\rangle = \langle -2, 2, -1 \rangle \]3. **Answer Identification:** - The correct choice is d. \( \langle -2, 2, -1 \rangle \).This problem explores the concept of average velocity in vector form,

The position of the particle at t = 1 is, r1=2,0,3. The position of the particle at t = 2 is,…

The positions of a particle at times t = 1,2 and 3 are given below. What is the average velocity of the particle in the time interval [1,3] ? %3D r(1) = (2,0, 3) r(2) = (1, 1, 1) r(3) = (-2, 4, 1) Select one: а. 5 b. (1, 1, 1) с. 3 d. (-2, 2, -1) e. (-1,3, 1)

The positions of a particle at times t = 1,2 and 3 are given below. What is the average velocity of the particle in the time interval [1,3] ? %3D r(1) = (2,0, 3) r(2) = (1, 1, 1) r(3) = (-2, 4, 1) Select one: а. 5 b. (1, 1, 1) с. 3 d. (-2, 2, -1) e. (-1,3, 1)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Cylinder B has a downward velocity vB = 6.2 ft/sec. Compute VA and VB/A. (VA = 2.07 ft/sec right, VB/A = 6.53 ft/sec) A B VB
3x The range of y = -3sin А. —3 <у <3 С. y S 3 В. —3
The position of a moving particle is given by s = 5+9t-t on the interval 0
Q.6.6
3x d dt & (5² d.) 2 dx An item moves along with velocity v(t) = 2+² -1 meters per second. Find the displacement during the time interval 2≤t≤s. a coordinate axis
Find the total differential. z = 10x6y7 dz =
The values of z and y vary together at a constant rate of change such that Ay = 0.5Ar. (This information applies to all three parts.) %3D a, Suppose the value of r varies from z 1.5 to z -3. Your classmate comes to you after calculating the change in a for this interval: Ar = 0.5(-3 - 1.5) = -2.25 Are they right? (Select the one best choice.) ONo. They calculated Ay instead. ONo. They used addition instead of subtraction. ONo. They subtracted in the wrong order. O Yes. This is the change in z. b. Suppose the change in e between two points in this relationship is 5. Another classmate has calculated the corresponding change in y: Ay = 5 Are they right? (Select the one best choice.) ONo. This is the change in z. ONo. The change in y should be the same sign as the change in x. O No. They divided instead of multiplied. O Yes. This is the change in y.
Which equation describes a linear function? OV = s3 O y = a O y = 2" O A= Tr2 INTL 10:28
The curve y= f(x) passes through the three points (1,3), (2,8.5), and (3,44). Estimate, as accurate as possible, dy /dx at x=1.5.
ds Find where Vt +s = 2s . %3D dt
Find the first derivative of the function below:
c. (x² – 9) + xy = 0 ху %3D С. dx