a particle moves along a line so that, at time t, its position is s(t)=8sin2t.
for what values of t does the particle change direction?

Question

a particle moves along a line so that, at time t, its position is s(t)=8sin2t. 
for what values of t does the particle change direction?

anonymous · Answer

where $\cos(2t)=0$ because that is where it goes from increasng to decreasing

anonymous · Answer

okay which is pi/4

anonymous · Answer

but how would i figure out the particles max velcoity? (Next part of the question)

anonymous · Answer

that is one point, yes

anonymous · Answer

velocity is given by $16\cos(2t)$ as it is the derivative of the position.  differentiate again to get the second derivative, that will tell you where the first derivative has a max

anonymous · Answer

which is -32sin2t?

anonymous · Answer

actually if it just says "what is the particles max velocity" you can reason that since $-1\leq \cos(x)\leq 1$ you must have the maximimum velocity is 16

anonymous · Answer

since that is the biggest $16\cos(2t)$ can be

anonymous · Answer

and how did u determine it is 16?

anonymous · Answer

yes your second derivative is right

anonymous · Answer

because the largest cosine can be is 1
so the largest 16cosine can be is 16

anonymous · Answer

how would i show my work for that?

anonymous · Answer

i would write that since $-1\leq \cos(x)\leq 1$ you get $-16\leq16\cos(2t)\leq 16$

anonymous · Answer

okay thanks

anonymous · Answer

how would i determine the max distance from the origin for the function, s=4sin4t