The equation of motion for a particle in meters at time t seconds is s (t) = sin (pi (t) / 6) + cos (pi (t) / 6), 0 is less then/equal to t is less then or equal to 2. What is the acceleration at the instant the velocity is 0

S (t) = sin (πt/6) + cos (πt/6)

Velocity = s' (t) = π/6 (cos (πt/6) - sin (πt/6))

When velocity = 0

cos (πt/6) - sin (πt/6) = 0

cos^2 (πt/6) - 2cos (πt/6) sin (πt/6) + sin^2 (πt/6) = 0

1 - 2cos (πt/6) sin (πt/6) = 0

1 - sin (πt/3) = 0

sin (πt/3) = 1

πt/3 = arcsin (1) = π/2

t = 1.5

acceleration = s'' (t) = - (π/6) ^2 (cos (πt/6) + sin (πt/6))

s'' (1.5) = - (π/6) ^2 (cos (π/4) + sin (π/4)) = - (π/6) ^2 (2/√2) = - 0.3877

accerelation = - 0.3877 meter/s^2