The displacement of an oscillating mass is given by x(t) = 20 cos( 5 t ). at time t = 0.5π s, what is the acceleration of the mass in m/s2?

The speed of the object is the 1st derivative of its displacement.

The acceleration is the 2nd derivative of the displacement.  That's also the first derivative of speed.  Either way you approach it, we have to take the displacement and differentiate twice.

Displacement = x(t) = 20 cos(5t) meters

Speed = x'(t) = -100 sin(5t) m/s

Acceleration = x''(t) = -500 cos(5t)  m/s²

At time  t=0.5π sec,

Acceleration = -500 cos(2.5π)  m/s²

cos (2.5π) = cos(0.5π) = zero

This is weird.  At  t=0.5π sec, the acceleration of the oscillating mass appears to be zero.

My math must be kerflooie, but I'm too tired right now to stay and pick at it.  I'll just resign myself to having my answer reported, and I hope whoever reports it will be kind enough to point out the error of my ways.

dopamine..

"it was found that some people who were taking the drug l-dopa to raise their levels of dopamine were developing schizophrenic-like symptoms supporting research a strength of the dopamine hypothesis is that there are many studies which have shown support for the neurochemical explanation."

okay i have so many questions. but the big one here is: um wt..f is this mess? ?