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

Chapter 2, Problem 122

(choose chapter or problem)

[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]