I need help answering these questions **Problem 3: Particle Motion Analysis**A particle's position along the x-axis as a function of time is given by \( x(t) = 7.0 - 12t + 2.5t^2 \), where \( x \) is in meters and \( t \) is in seconds.**Part (a):** Determine the particle's initial position, initial velocity, and acceleration. You can compare it to a kinematics equation or simply use calculus.**Part (b):** Note that the initial velocity is negative. At what time will the particle start moving in the positive direction—i.e., when will its velocity be zero, just about to become positive?**Part (c):** Where will the particle be at that time?

Answered: Image /qna-images/answer/a34e5b52-f72a-4bdc-8745-81bc79d84d69.jpg

3. A particle's position along the x-axis as a function of time is given by x(t) = 7.0- 12t + 2.5t² where x is in meters and t is in seconds. a) Determine this particle's initial position, its initial velocity, and its acceleration. You can compare it to a kinematics equation or simply use calculus. b) Note that the initial velocity is negative. At what time will the particle start moving in the positive direction - that is, when will its velocity be zero, just about to become positive? c) Where will the particle be at that time?

3. A particle's position along the x-axis as a function of time is given by x(t) = 7.0- 12t + 2.5t² where x is in meters and t is in seconds. a) Determine this particle's initial position, its initial velocity, and its acceleration. You can compare it to a kinematics equation or simply use calculus. b) Note that the initial velocity is negative. At what time will the particle start moving in the positive direction - that is, when will its velocity be zero, just about to become positive? c) Where will the particle be at that time?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 26P: PROBLEM A race car starting from rest accelerates at a constant rate of 5.00 m/s2, (a) What is the...

See similar textbooks

Related questions

Q: Those answers were incorrect

Q: Q4. Convert these into proper vector notation: Westward velocity of 42 km/h. Position 6.5 measured…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: This answer is incorrect, was there a possible step that was missed?

A: Initial temperature =100CFinal temperature = 92 C

Q: In the higure. the long straight wire carries a current of 30 A and the rectangular loop carries a…

A: Scenario - A loop and a wire are placed in Y-Z plane such that loop is a little far from the wire.…

Q: How much does it cost to power a refrigerator for 30 days if it is rated at 200 Watts and the power…

A: Electrical energy (E) use equals the power (P) of the object multiplied by the amount of time (t)…

Q: I need part D, thank you!

Q: 2) A 2 kg block slides with initial speed 3 m/s at a height 1 m above ground down an irregularly…

Q: A cyclist, starting from rest, travels in a straight line for 10 minutes. 1. During the first 2.0…

A: Given the uniform acceleration is 0.067 m.s-2 for the first two minutes. Therefore the velocity for…

Q: A 1.0-kilogram mass gains kinetic energy as it falls freely from rest a vertical distance d. How far…

A: Given data: Initial velocity (Vi) = 0 m/s Mass (m) = 1.0 kg Vertical distance (h) = d New mass (m')…

Q: Thank you,

Q: E1.A horizontally directed force of 25.0 N is used to pull a box a distance of 1.5 m across a…

A: Dear Student, As per our company policy, I am allowed to answer only first 3 subparts. So, kindly…

Q: 1. What is the x component of A'? 2. What is the y component of A'? 3. What is the y component of B?

A: As per our guidelines, we are supposed to answer only first three subparts in case of multiple…

Q: A cannonball is launched diagonally with an initial horizontal velocity of 38.0m/s. Label the…

A: (1) Given: The initial horizontal velocity is 38.0 m/s. The angle of launch is 23.0°.

Concept explainers

Units and Dimensions

These are generally defined as the terms which precede or describes the dimensions further. These are also further divided into two parts namely fundamental units and the derived units.

Question

I need help answering these questions

**Problem 3: Particle Motion Analysis**

A particle's position along the x-axis as a function of time is given by \( x(t) = 7.0 - 12t + 2.5t^2 \), where \( x \) is in meters and \( t \) is in seconds.

**Part (a):**
Determine the particle's initial position, initial velocity, and acceleration. You can compare it to a kinematics equation or simply use calculus.

**Part (b):**
Note that the initial velocity is negative. At what time will the particle start moving in the positive direction—i.e., when will its velocity be zero, just about to become positive?

**Part (c):**
Where will the particle be at that time?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A student drives a moped along a straight road as described by the velocity-versus-time graph in Figure P2.12. Sketch this graph in the middle of a sheet of graph paper. (a) Directly above your graph, sketch a graph of the position versus time, aligning the time coordinates of the two graphs. (b) Sketch a graph of the acceleration versus time directly below the velocity-versus-time graph, again aligning the time coordinates. On each graph, show the numerical values of x and ax for all points of inflection. (c) What is the acceleration at t = 6.00 s? (d) Find the position (relative to the starting point) at t = 6.00 s. (e) What is the mopeds final position at t = 9.00 s? Figure P2.12
Problems 74 and 75 are paired. 74. N A classroom clock has a small magnifying glass embedded near the end of the minute hand. The magnifying glass may be modeled as a particle. Class begins at 7:55 and ends at 8:50. The length of the minute hand is 0.300 m. a. Find the average velocity of the magnifying glass at the end of the minute hand using the coordinate system shown in Figure P3.74. Give your answer in component form. b. Find the magnitude and direction of the average velocity. c. Find the average speed and in the CHECK and THINK step, compare to the average velocity.
A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by x(t)=[(0.02m/s3)t3(0.35m/s2)t2+(1.75m/s)t2.00m]i a. Find an expression for the dancers velocity as a function of time. b. Graph the velocity as a function of time for the 14 s over which the dancer performs (the dancer begins when t = 0) and use the graph to determine when the dancers velocity is equal to 0 m/s.
(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in the following figure. (b) Identify the time or times (ta,tb,tcetc.) at which the instantaneous velocity has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?
A speedboat travels in a straight line and increases in speed uniformly from i = 20.0 m/s to f = 30.0 m/s in displacement x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of i, f, and x. (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
Two students air on a balcony a distance h above the street. One student throws a ball vertically down-ward at a speed v0; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of v0, g, h, and t. (a) Write the kinematic equation for the y-coordinate of each ball, (b) Set the equations found in part (a) equal to height 0 and solve each for t symbolically using the quadratic formula. What is the difference in the two balls' time in the air? (c) Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground, (d) How far apart are the balls at a time t after they are released and before the strike the ground?
A particle starts from the origin with velocity 5im/s at t = 0 and moves in the xy plane with a varying acceleration given by a=(6tj), where a is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function of time. (b) Determine the position of the particle as a function of time.
A speedboat travels in a straight line and increases in speed uniformly from vi = 20.0 m/s to vf = 30.0 m/s in a displacement x of 200 m. We wish to find the time interval required for the boat to move through this displacement. (a) Draw a coordinate system for this situation. (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of vi, vf, and x. (e) Substitute numerical values to obtain the acceleration numerically. (f) Find the time interval mentioned above.
Astronauts on a distant planet toss a rock into the air. With the aid of a camera that takes pictures at a steady rate, they record the rocks height as a function of time as given in the following table. (a) Find the rocks average velocity in the time interval between each measurement and the next. (b) Using these average velocities to approximate instantaneous velocities at the midpoints of the time intervals, make a graph of velocity as a function of time. (c) Does the rock move with constant acceleration? If so, plot a straight line of best fit on the graph and calculate its slope to find the acceleration.
Figure P4.8 shows the motion diagram of two balls, one on the left and one on the right. Each ball starts at a point labeled i. The ball on the left is released and falls straight down. At the same time, the ball on the right is launched horizontally and follows the path shown. a. Use the given coordinate system to write the position of points i, C, E, G, and K in component form for each ball. b. Find the displacement of each ball from i to points C, E, G, and K. c. Compare your answers for the two balls in part (b). What similarities do you notice? FIGURE P4.8 Problems 8 and 26.
Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a hiker hears a rock break loose from a height of 105 m. He can't see the rock right away but then does, 1.50 s later. (a) How far above the hiker is the rock when he can see it? (b) How much time does he have to move before the rock hits his head?
The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a persons bank account balance. The units of x would be dollars (), and velocity v would give the rate at which the balance changes (in units of, for example, /month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management, leads to no net change in the account balance so that v0 = 0. Unfortunately, management worsens over time so that a = 2.5 102 /month2. Assuming a is constant, find the amount of time in months until the bank account is empty