# ?[T] Let $$\mathbf{r}(t)=\left\langle t, 2 t^{2}, 4 t^{2}\right\rangle$$ be the position

Chapter 2, Problem 122

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[T] Let $$\mathbf{r}(t)=\left\langle t, 2 t^{2}, 4 t^{2}\right\rangle$$ be the position vector of a particle at time t (in seconds), where $$t \in[0,10]$$ (here the components of r are expressed in centimeters).

a. Find the instantaneous velocity, speed, and acceleration of the particle after the first two seconds. Round your answer to two decimal places.

b. Use a CAS to visualize the path of the particle defined by the points $$\left(t, 2 t^{2}, 4 t^{2}\right)$$ , where $$t \in[0,60]$$.

Text Transcription:

r(t) = langle t, 2t^2, 4t^2 rangle

t in [0,10]

(t, 2t^2, 4t^2)

t in [0,60]

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