Quick question about a simple harmonic motion problem

AI Thread Summary
The position of a particle is defined by the equation x = 4.6 cos(πt). The maximum speed and acceleration were determined using the first and second derivatives, resulting in v = -4.6(π)sin(πt) and a = -4.6(π^2)cos(πt). For the specific case when x = 2.3 m, the time calculated was 19.098593 seconds, leading to a speed that was confirmed as correct. The discussion clarified that acceleration, being a vector quantity, does not require taking the absolute value, affirming that -22.7 m/s² is indeed the correct answer. The final confirmation emphasized the importance of understanding vector quantities in physics.
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Homework Statement



The position of a particle is given by x = 4.6 cos (pi)t, where x is in meters and t is in seconds.

(a) Find the maximum speed and maximum acceleration of the particle.

I've already solved these by finding the first and second derivatives of the above x.

v = -4.6(pi)sin(pi*t)
a = -4.6(pi^2)cos(pi*t)(b) Find the speed and acceleration of the particle when x = 2.3 m.

I've figured out the speed by using the position equation to find the time where x = 2.3m. This is at 19.098593s. I solved that, and took the absolute value to find its speed.

Now, I'm stuck on acceleration. I only have one more try left on my homework and I need to make sure it's correct. I solved for acceleration the same way and got -22.7 m/s^2. I took the absolute value of this and plugged it in, and it's incorrect. Was I supposed to take the absolute value? Is -22.7 m/s^2 actually the correct answer?
 
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Yes, because acceleration is a vector quantity and can be negative.
 
Great, it was correct. Thank you!
 

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