How would I solve this:

-A particle moves along a line so that, at time t, its position is s(t)=8 sin2t.

a) For what values of t does the particle change direction?

b) What is the particle's maximum velocity?

1 answer

a) The particle changes direction when the sine function changes sign, which occurs when t = (n + 1/2)π, where n is an integer.

b) The maximum velocity of the particle is 8, which occurs when the sine function is equal to 1, which occurs when t = nπ, where n is an integer.