Define s(t)= 2sin(t) + sqrt(2t) to be the position of a particle after time t in seconds. Bound t by the domain 0 is less than or equal to t, t is less than or equal to 2pi.
a. Find the velocity and acceleration functions of s(t).
b. Find when the particle is at rest.
c. Find the times when the particle is moving forward and moving backward from its initial position.
A. I got s'(t)=v(t)= 2cos(t) + 1/sqrt(t)
and s''(t)=a(t)= -2sin(t) + 1/(2)sqrt(t^3)
Is this correct so far?
B. I set v(t)=0, so: 2cos(t) + 1/sqrt(t) = 0
How do I solve for cos(t)?
C. I have no idea where to begin.