Need help setting up basic dynamics problem

[fletch]

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point a oscillates with accel of a=2880-144x. Magnitude of velocity is 11in/s when x=20.4in. Determine the max velocity of A & two positions at which velocity is zero.

Why am I getting this wrong :( It seems so easy

integrate a=2880-144x to get v, plug in 11in/s and 20.4in as the initial values, solve for the constant and you get the velocity equation. From the acceleration equation you know there is a critical value at x=20in, so plugging x=20 to the velocity equation should give you the max velocity, and the other part is just finding the zeroes of v=...is that the right setup?

 

[lightgrav]

Your initial value (v=11in/s) is NOT QUITE at maximum-velocity
location, so if you did not include a phase angle or time-offset,
(ending up with 20.917...) that might be your error.

umm, how do you know you're getting it wrong?

 

[quicknote]

It looks like you are on the right track with your approach to solving this dynamics problem. However, it is important to carefully consider the units being used in the problem. The acceleration is given in inches per second squared, while the velocity is given in inches per second. This means that your velocity equation should have units of inches per second, not just a number.

Additionally, when solving for the constant in the velocity equation, make sure to use the correct units in your calculations. In this case, the units for the constant should be inches per second squared.

Once you have the correct velocity equation, you can use it to find the maximum velocity. This will occur at the point where the acceleration is equal to zero, which you correctly identified as x=20 inches. Plugging this value into your velocity equation will give you the maximum velocity for point A.

To find the two positions at which the velocity is zero, you can set the velocity equation equal to zero and solve for x. This will give you two values of x, one on either side of the maximum velocity point, where the velocity is equal to zero. This is because the velocity will change from positive to negative as it passes through the maximum.

It is possible that your initial setup was incorrect due to incorrect unit conversions or not considering the critical point at x=20 inches. Make sure to carefully check your calculations and units to ensure that your setup is correct. Good luck with your problem!