Question

The position of an object is given by the expression s=5−2sint . Which of the following is the object’s jerk at time t=2π3 ? (1 point) Responses −1 - 1 −3–√ - 3 0 0 3–√ 3 1

Answer 1

To find the object's jerk, we need to find the third derivative of the position function with respect to time.

Given the position function s = 5 - 2sin(t), let's find the derivatives step by step:

First derivative:
s' = d/dt(5 - 2sin(t))
= -2cos(t)

Second derivative:
s'' = d/dt(-2cos(t))
= 2sin(t)

Third derivative:
s''' = d/dt(2sin(t))
= 2cos(t)

Now, we need to evaluate the third derivative at t = 2π/3:

s'''(2π/3) = 2cos(2π/3)
= 2cos(120°)
= 2(-1/2)
= -1

Therefore, the object's jerk at time t = 2π/3 is -1.