### Problem StatementThe position vector of a particle is given by:\[ \mathbf{r} = 11t\mathbf{i} + 2.0t^2\mathbf{j} - 0.9(t^3 - 5)\mathbf{k} \]where \( t \) is the time in seconds from the start of the motion and \(\mathbf{r}\) is expressed in meters. For the condition when \( t = 4 \) seconds, determine the power \( P \) developed by the force:\[ \mathbf{F} = 36\mathbf{i} - 21\mathbf{j} - 46\mathbf{k} \, \text{N} \]which acts on the particle.### SolutionAnswer: \( P \) = \[ \underline{\makebox[3cm]{}} \] kW### ExplanationTo determine the power \( P \) developed by the force on the particle, follow these steps:1. **Find the velocity vector \(\mathbf{v}\) by differentiating the position vector \(\mathbf{r}\) with respect to time \( t \).**\[ \mathbf{v} = \frac{d\mathbf{r}}{dt} \]2. **Evaluate the velocity vector \(\mathbf{v}\) at \( t = 4 \) seconds.**3. **Calculate the instantaneous power \( P \) using the formula:**\[ P = \mathbf{F} \cdot \mathbf{v} \]Here, \( \cdot \) represents the dot product of the force vector and the velocity vector.4. **Convert the power to kilowatts (kW) if necessary.**

Answered: Image /qna-images/answer/6d3afde6-02c4-4e89-bde5-0165895e4070.jpg

The position vector of a particle is given by r = 11ti + 2.0t²j - 0.9(t3-5)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition when t = 4 s, determine the power P developed by the force F = 36i - 21j - 46k N which acts on the particle. Answer: P = i kW

The position vector of a particle is given by r = 11ti + 2.0t²j - 0.9(t3-5)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition when t = 4 s, determine the power P developed by the force F = 36i - 21j - 46k N which acts on the particle. Answer: P = i kW

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

See similar textbooks

Similar questions

An object with a mass of 0.45 kg is released from rest while immersed within a fluid. It reaches a speed of 50.6 percent its maximum speed in a time of 0.5 seconds. What is the object's terminal speed if the resistive force acting is given by; R = -bv ? (Assume that the gravitational force also acts)
F = (C · t²) Q14. As shown in the image below, the force acting on the box is N, where constant C = 10 and t is time in s. Determine the magnitude of the total impulse (in N.s) done by force F to the box during the period from t = 0 to t = 1.5 s. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. F Your Answer: Answer 3 5 4
2/38 The aerodynamic resistance to motion of a car is nearly proportional to the square of its velocity. Ad- ditional frictional resistance is constant, so that the acceleration of the car when coasting may be written = -C₁-C₂², where C₁ and C₂ are constants which depend on the mechanical configuration of the car. If the car has an initial velocity vo when the en- gine is disengaged, derive an expression for the dis- tance D required for the car to coast to a stop. a V.
Plssss kindly answer it
4. Carriage B is loaded with box A as shown in the figure. Find the acceleration of caravan B and box A.
determine whether there will be sliding between objects or not? What are the decisive factors? How do you approach the solution of such a problem? Group 3: 1-) At t=0, A4 has a downward velocity of 0.8 m/s. In addition, it has an upward constant acceleration of 2 m/s². At t=2 secs, what are the velocity and acceleration of B and the total distance travelled by each block? B XB 2-) Block B is initially at rest. When block B has a velocity of 3 m/s; calculate the change in position of block B. Use energy-work methods to solve this problem. 3-) On an inclined surface, assume one block is positioned on the top of another one. Taking relative accceleration principles into account, how could you draw the free body diagram(s) of such a problem? What should your strategy be in this case? You can draw an example and show your explanations without solving the problem. I
The position of a particle as a function of time t, is given by x(t) = at +bt² - ct³ where a, b and care constants. When the particle attains zero acceleration, then its velocity will be? A B с D a+ E + a+ a+ b² 4c b² 2c b² 3c
At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.78i m. By time t = 0.019 s, its position vector has become (4.96i + 0.52j) m. Determine the magnitude Vay of its average velocity during this interval and the angle e made by the average velocity with the positive x- axis. Answers: Vav Ꮎ = = i i m/s
The angle of rotation of a body is given by the equation, e= 3t3 + 4t2-6t+9, where eis expressed in radians and t in seconds, Find (i) Angular velocity and (ii) Angular acceleration of the body when t = 0 and t = 4 sec.
The velocity of a particle which moves along the s-axis is given by s = 49 - 6t2 m/s where t is in seconds. Calculate the displacement As of the particle during the interval from t = 0.7 s to t = 3.5 s. Answer: As = i ! m
The position of a particle as a function of time t, is given by x(t) = at +bt² - ct³ where a, b and care constants. When the particle attains zero acceleration, then its velocity will be? A B с D a+ E + a+ a+ b² 4c b² 2c b² 3c
The position of a particle that is moving along a horizontal x-axis is given by x = (t3 - 3t2-5) m (x is positive to the right). Calculate the total distance traveled by the particle for the time interval from t = 0s to t = 4 s. O 12 m O 16 m 18 m 24 m O