The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 3t3 − 6t meters for t ≥ 0

Question

The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 3t³ − 6t meters

 for t ≥ 0

(a)

Determine the velocity of the bird (in m/s) at t = 1

 s.

  ? m/s

(b)

Determine the acceleration of the bird (in m/s²) at t = 1

 s.

 ? m/s²

(c)

Determine the acceleration of the bird (in m/s²) when the velocity equals 0. (Round your answer to two decimal places.)

? m/s²

Answer 1

(a) Velocity v(t) = s'(t) = 9t² - 6; v(1) = 9 - 6 = 3 m/s

(b) Acceleration a(t) = v'(t) = 18t; a(1) = 18 m/s²;

(c) v(t) = 0; 9t² - 6 = 0; t = √6/3 = 0.82 s

a(0.82) = 6√6 m/s² = 14.7 m/s².