Calculus
posted by Rudy on .
A particle moves along a horizontal line so that at any time t its position is given by x(t)=costt. Time is measured in seconds and x is measured in meters.
a.) Find the velocity as a function t. Use your answer to determine the velocity of the particle when t=pi/6 seconds. Indicate units of measure.
b.) Find the acceleration as a function of the time t. Use your answer to determine the velocity of the particle when t=pi/6 seconds. Indicate units of measure.
c.) What are the values of t,0≤t≤2pi, for which the particle is at rest?
d.) What are the values of t, 0≤t≤2pi, for which the particle moves to the right?
e.) At t=pi/6 seconds, is the particle speeding up or slowing down? Justify your answer.

x = cos t  t
dx/dt = v = sin t  1
sin pi/6 = sin 30 = 1/2
so
v = 1.5
a = dv/dt = cos t
I think you want the acceleration a = sqrt3/2
when is v = 0 ?
when sin t = 1 which is t = 3 pi/2
when is v >0? when sin t <1 which is never
when t = pi/6 , a is negative so v is getting less negative so slowing down