When does the particle reach its maximum x position?

[suxatphysix]

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

 

[blochwave]

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

 

[Shooting Star]

(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.

 

[suxatphysix]

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.

 

[blochwave]

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

 

[Shooting Star]

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?