For t≥0, the position of a particle moving along the x-axis is given by x(t)=sint−cost . What is the acceleration of the particle at the point where the velocity is first equal to 0 ?

Question

For  the position of a particle moving along the x-axis is given by . What is the acceleration of the particle at the point where the velocity is first equal to 0 ?

Answer 1

x(t) = sint - cost

x'(t) = v(t) = cost + sint (When does this equal zero?)

cost + sint = 0

cost = -sint

t = 3π/4 (cos(3π/4) = -sin(3π/4) = -√2/2)

a(t) = -sint + cost

a(3π/4) = -(√2/2) + -(√2/2)

=-2√2/2

=-√2