Question

The position of a particle moving in a straight line is given by s(t) = 2sint - cost , from 0 to 2 pi
where s is the displacement in metres and t is the time in seconds. Find the absolute max and absolute min displacements.

Answer 1

s'(t) = 2cost + sint
= 0 for a max/min
sint = -2cost
sint/cost = -2
tant = -2
t = π - 1.107 = 2.0344 or
t = 2π - 1.107 = 5.176

s(2.0344) = 2.236
s(5.176) = -2.236

so the max is ...
and the min is ....