Velocity Vectors: Speed & Acceleration

[joemama69]

Homework Statement

A particle moves with position function r(t) = t lnt$$\hat{i}$$ + t$$\hat{j}$$ + e^-t$$\hat{k}$$
Find the velocity vector, speed, and acceleration.

Homework Equations

The Attempt at a Solution

$$\hat{v}$$(t) = (1 + lnt)$$\hat{i}$$ + $$\hat{j}$$ - e^-t$$\hat{k}$$
$$\hat{a}$$(t) = 1/t $$\hat{}i$$ + e^-t $$\hat{k}$$
$$\left\|$$v(t)$$\right\|$$ = $$\sqrt{lnt + e^(-2t) + 2lnt + 2}$$

 

[Mark44]

v(t) and a(t) look good, but you're a little off on ||v(t)||. The ln t term under the radical should be (ln t)². Maybe you just forgot to put it in while writing the LaTeX code.