Why Does the Particle Not Move in the +x Direction at t = 0.13351 Seconds?

AI Thread Summary
The position of the particle is defined by the equation x = 6*cos(3πt), and the goal is to determine when it first reaches x = 0 while moving in the +x direction. The calculated time of t = 0.13351 seconds is incorrect because it does not account for the particle's velocity at that moment. To find the correct time, one must also consider the velocity, which is derived from the position function. The particle is moving in the +x direction when its velocity is positive, indicating that further analysis of the velocity function is necessary to determine the correct time.
inversesine
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Homework Statement



The position of a particle is given in cm by x = 6*cos(3πt), where t is in seconds.

What is the first time that the particle is at x = 0 and moving in the +x direction?



Homework Equations





The Attempt at a Solution



I set x=0, and divided 0 by 6, resulting in 0. From there, I took the inverse cosine of each side, leaving me with the equation (π/2)=3πt. Then I divided (π/2) by 3π, and was left with a t value of .13351 seconds. The problem is that when I submit that answer, it is incorrect.
 
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inversesine said:

Homework Statement



The position of a particle is given in cm by x = 6*cos(3πt), where t is in seconds.

What is the first time that the particle is at x = 0 and moving in the +x direction?



Homework Equations





The Attempt at a Solution



I set x=0, and divided 0 by 6, resulting in 0. From there, I took the inverse cosine of each side, leaving me with the equation (π/2)=3πt. Then I divided (π/2) by 3π, and was left with a t value of .13351 seconds. The problem is that when I submit that answer, it is incorrect.

You ignored that the particle moves in the +x direction: the velocity is positive.

How do you get the velocity of the particle at time t?

ehild
 

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