A particle undergoing simple harmonic motion has initial displacement 1, initial velocity 2, and initial acceleration -12. Compute the displacement and acceleration when the velocity is .

First, since the initial displacement is 1 we have,

Next, since the initial velocity is 2 we have,

Finally, since the initial acceleration is we have,

Now, using the first equation we plug the value of into the third equation,

Then, from the second equation

Since we now have values for and we can compute ,

We then compute the value of ,

So now we have the complete equation of motion

Therefore, we can compute the quantities the problem requests,

Finally, this gives us

and,