When does the particle reach its maximum x position?

In summary, the conversation is discussing a particle's position on the x-axis over time, given an equation with numerical values for c and b. The conversation goes on to discuss finding the maximum positive x position and acceleration at a specific time. The solution involves taking the derivative and setting it equal to zero. There is also a discussion about the possibility of c or b being equal to zero in the equation.
  • #1
suxatphysix
30
0

Homework Statement



The position of a particle moving along the x-axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds.

For the following, let the numerical values of c and b be 3.5 and 1.0 respectively.

(b) At what time does the particle reach its maximum positive x position?

(f) What is its acceleration at at t = 1.0 s?

Homework Equations





The Attempt at a Solution



For (b) I tried plugging in numbers starting at 1 until the the result started to decrease. I am not sure if I must take the derivative first though.

For (f) I am assuming you take the second derivative of the equation. Is the derivative not 2-6bt ? Answer I got : -4
 
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  • #2
Well what does dx/dt represent? The rate of change.

now I can't tell, is it sposed to be x=c*t^2-b*t^3? I'm assuming or else it's a terribly uninteresting problem

So for b

dx/dt=2*c*t-3*b*t^2

you're looking for a maximum, so you set dx/dt=0 and solve for t. It's a quadratic equation so there are two solutions

How do you decide which one's right?

You had the right idea for f, but the second derivative is 2c-6bt=a
 
  • #3
(Use the symbol ^ for power.)

x = ct^2 - bt^3.

b. At the extreme +ve posn the v would be 0, so, yes, you should find dx/dt.

f. 2c-6bt. Now find answer.
 
  • #4
Thank you, I got (f) right. But for (b) I have another question. For the quadratic equation does c = 0? To decide which one is right, you pick the positive one because time cannot be negative. For my answer I am getting 0. This doesn't sound right.
 
  • #5
it's possible if the initial velocity is negative and it only gets more negative, then the initial position should be the biggest it ever gets
 
  • #6
suxatphysix said:
But for (b) I have another question. For the quadratic equation does c = 0? To decide which one is right, you pick the positive one because time cannot be negative. For my answer I am getting 0. This doesn't sound right.

For elementary problems like these, unless otherwise mentioned, the co-efficients will not be equal to zero. But it's shows your interest that you have asked, and blochwave has given you the answer. You should then also ask what if c=0, both=0.

Assuming non-zero b and c, have you solved it?
 

What is 1D kinematics?

1D kinematics is a branch of physics that deals with the motion of objects in one dimension, specifically along a straight line. It involves studying the position, velocity, and acceleration of objects in relation to time.

What are the basic equations of 1D kinematics?

The basic equations of 1D kinematics are:

1. Position (x) = Initial position (x0) + Velocity (v) * Time (t)

2. Velocity (v) = Initial velocity (v0) + Acceleration (a) * Time (t)

3. Final velocity (v)² = Initial velocity (v0)² + 2 * Acceleration (a) * Change in position (Δx)

4. Change in position (Δx) = Initial velocity (v0) * Time (t) + 1/2 * Acceleration (a) * Time (t)²

5. Final velocity (v) = Initial velocity (v0) + 1/2 * Acceleration (a) * Time (t)

What are the different types of motion in 1D kinematics?

The different types of motion in 1D kinematics include:

1. Uniform motion - when an object moves with a constant velocity

2. Uniformly accelerated motion - when an object moves with a constant acceleration

3. Free fall - when an object is only influenced by the force of gravity

4. Projectile motion - when an object is thrown or launched at an angle with a combination of horizontal and vertical motion

How is time represented in 1D kinematics?

In 1D kinematics, time is typically represented by the variable "t" and is measured in seconds. It is a crucial factor in determining the position, velocity, and acceleration of an object.

What are some real-life applications of 1D kinematics?

1D kinematics has numerous real-life applications, including:

1. Calculating the speed and distance traveled by a car on a straight road

2. Predicting the height and landing location of a ball thrown in the air

3. Understanding the motion of a roller coaster along its track

4. Analyzing the motion of projectiles, such as a baseball being hit by a bat

5. Determining the acceleration of an object in free fall, such as a skydiver

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