Question

a particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t3 − 6t2 9t

Answer 1

The particle's motion is described using the equation s = f(t), where t is time and s is the position of the particle. At t = 3 s, the velocity of the particle is 15 m/s and the acceleration is negative, indicating that the particle is slowing down. The acceleration vector being negative means the particle is decelerating.

Step-by-step explanation:

In this question, the particle's motion is described by the equation s = f(t), where s is the position of the particle and t is time. The function f(t) = t3 - 6t2 + 9t gives the position of the particle at any given time. The particle's velocity and acceleration can be determined by taking derivatives of the position equation.

At t = 3 s, the velocity is v(3 s) = 15 m/s and the acceleration is negative. This means that the particle has reduced its velocity and is slowing down. The acceleration vector being negative indicates that the particle is decelerating.