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

\[\huge s(t) = \sin({\pi t \over 6}) + \cos({\pi t \over 6})\]
\[\huge v(t) = {ds \over dt} = {\pi \over 6} \cos({\pi t \over 6}) - {\pi \over 6}\sin({\pi t \over 6})\]
\[\huge a(t) = {dv \over dt} = -({\pi \over 6 })^2 \sin({\pi t \over 6})-({\pi \over 6 })^2 \cos({\pi t \over 6})\]

let v = 0 to get t

then substitute with this t in the function of a

Answer 2

then
t=3/2
a=-0.388m/s^2