Suppose an object is moving along a horizontal coordinate line with distance formula

Question

Suppose an object is moving along a horizontal coordinate line with distance formula

s(t) = t³ - t² (in feet）

where t ≥ 0 is in seconds.

(a) Find the velocity v(t) and acceleration a(t)

• Include units!

(b≥) When is the object moving to the right?

(c) When is the acceleration positive?

Answer 1

s(t) = t³ - t²

Velocity = s'(t) = 3t² - 2t ft/sec

3t² - 2t = 0

t(3t - 2) = 0 t = 0 or 2/3

When 0 < t < 2/3, s'(t) < 0 (so the object is moving to the left)

When t > 2/3, s'(t) > 0 (so the object is moving to the right)

Acceleration = s"(t) = 6t - 2 ft / sec²

Acceleration is positive when 6t - 2 > 0. So, t > 1/3 sec