A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = cos(t), where t is in seconds and x is in centimeters.
(a) Find the velocity and acceleration at time t.
v(t) = -sin(t)
a(t) = -cos(t)
(b) Find the position, velocity, and acceleration of the mass at time t = 53/6.
x(53/6) = cos(53/6)
v(53/6) = -sin(53/6)
a(53/6) = -cos(53/6)
In what direction is it moving at that time? Since x(53/6) > 0, the particle is moving to the right.