# If the position of a particle is given

(a) If the position of a particle is given by $x=20t-5t^{3}$, where $x$ is in meters and $t$ is in seconds, when, if ever, is the particle’s velocity zero? (b) When is its acceleration a zero? (c) For what time range (positive or negative) is $a$ negative? (d) Positive? (e) Graph x(t), v(t), and a(t).

### e)

Position vs Time

Velocity vs Time

Acceleration vs Time