An electron moving along the $x‐$axis has a position given by, $x=16t{e}^{\left(-\mathrm{t}\right)} \mathrm{m}$ where $t$ is in seconds. How far is the electron from the origin when it momentarily stops?

The displacement of a particle moving along an $x‐$axis is given by $x=18t+5t^2$, where $x$ is in meters and $t$ is in seconds.

Calculate (a) the instantaneous velocity at $t=2.0 \mathrm{s}$ and (b) the average velocity between $t=2.0 \mathrm{s}$ and $t=3.0 \mathrm{s}$.

The position of a particle moving along an $x‐$axis is given by $x=12t^2-2t^3$, where $x$ is in meters and $t$ is in seconds. Determine

(a) the position

(b) the velocity and

(c) the acceleration of the particle at $t=3.5 \mathrm{s}$

(d) What is the maximum positive coordinate reached by the particle and

(e) at what time is it reached?

(f) What is the maximum positive velocity reached by the particle and

(g) at what time is it reached?

(h) What is the acceleration of the particle at the instant the particle is not moving (other than at $t=0$)? (i) Determine the average velocity of the particle between $t=0$ and $t=3 \mathrm{s}$.

(a) If the position of a particle is given by $x=25t-6.0t^3$, where $x$ is in meters and $t$ is in seconds, when, if ever, is the particle's velocity $v$ zero?

(b) When is its acceleration $a$ zero? For what time range (positive or negative) is $a$

(c) negative and

(d) positive?

(e) Graph $x\left(t\right)$, $v\left(t\right)$ and $a\left(t\right)$