What is the position of a particle at maximum speed?

In summary, the position of the particle when it achieves its maximum speed in the positive x direction can be found by taking the derivative of the position function, which is 6.0t^2 - 1.0t^3, and setting it equal to zero to find the maximum velocity. This can then be used in conjunction with the motion equations to solve for the position.
  • #1
jrrodri7
31
0

Homework Statement


The position of a particle moving along the x-axis is given by

x = 6.0t^{2} - 1.0t^{3} , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?


Homework Equations



motion equations and derivative/integration ideas from motion.

The Attempt at a Solution

 
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  • #2
You forgot to attempt a solution. Please try?
 
  • #3
How do you think you would get velocity from that expression?
 
  • #4
You are given position as a function of time. How is velocity related to position? I think you mentioned derivatives/integrals as things to use.
 
  • #5
ya i figured the derivative of position is velocity right, but I tried doing that and then using that as galileo's equation of motion, substituting the 12 and 3 for velocity and acceleration...but i kept getting numbers that didn't make sense.
 
  • #6
Yes, the derivative of the position is the velocity. Now how would you maximize it? Your description of what you did isn't very clear. Can you write it out completely, showing those numbers that 'don't make sense'?
 
  • #7
the derivative is 12t - 3t^(2). That is velocity, now to maximize the equation take the derivative of it? and use that to plug into the other one?
 
  • #8
Yes, to maximize something you take it's derivative and set it equal to zero. In this case you are setting the acceleration equal to zero. At maximum velocity, the acceleration is zero.
 

What is the equation of motion problem?

The equation of motion problem is a physics problem that involves finding the relationship between an object's position, velocity, and acceleration over time. It is used to predict the motion of an object based on known initial conditions and any forces acting upon it.

What are the three main equations of motion?

The three main equations of motion are the displacement equation (Δx = v0t + ½at2), the velocity equation (v = v0 + at), and the acceleration equation (v2 = v02 + 2aΔx). These equations can be used to solve for an object's position, velocity, and acceleration at any given time.

What are the key concepts involved in solving an equation of motion problem?

The key concepts involved in solving an equation of motion problem are position, velocity, acceleration, time, and initial conditions. It is important to understand the relationships between these variables and how they are represented in the equations of motion.

How do you approach solving an equation of motion problem?

To solve an equation of motion problem, you should first identify the known and unknown variables, and then choose the appropriate equation to solve for the unknown variable. You may need to rearrange the equation or use algebra to isolate the unknown variable. Finally, plug in the known values and solve for the unknown variable.

Can the equation of motion be used for any type of motion?

The equation of motion can be used for any type of motion that is constant or can be broken down into smaller segments of constant motion. However, it may not accurately predict the motion of objects with varying acceleration or non-constant forces acting upon them.

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