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 i s less then or equal to 2. What is the acceleration at the instant the velocity is 0
1 answer:
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
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