# Velocity vectors

## 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.

## 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)$$\right\|$$ = $$\sqrt{lnt + e^(-2t) + 2lnt + 2}$$

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