Question

A particle moves along a line so that at time t, its position is s= 4 sin 4t. a) when does the particle change direction?

Answer 1

if we assume t = 0 is the start, then it will change when we get the max value of 4sin(4t)
we know the max value of sin(x) = 1 so max 4sin(4t) = 4
solve this
sin(4t) = 1
this happens when 4t = pi/2 so t= pi/8

Answer 2

thanks a lot!

Answer 3

np

Answer 4

what I showed will give you the first time it changes direction
this is every time it changes direction
\[4t=\frac{\pi}{2}+\pi*k\]
where K is a whole number

\[t=\frac{\pi}{8}+\frac{\pi}{4}k\]

Answer 5

do you understand all the steps?

Answer 6

wait.. i will try to do it myself..

Answer 7

I understand.. but the correct answer are \[t=\frac{ \pi }{ 4 }+\pi K, t=\frac{ 3\pi }{ 4 }+\pi K \] for positive integers K

Answer 8

hmm i guess it changes directions when 4sin(4t) = 0?

Answer 9

that does not make sense to me. sorry I told you the wrong think...