Question

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

Answer 1

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