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# A particle moves according to a law of motion $s = f(t), t \ge 0,$ where $t$ is measured in seconds and $s$ in feet.(a) Find the velocity at time $t.$(b) What is the velocity after I second? (c) When is the particle at rest?(d) When is the particle moving in the positive direction?(e) Find the total distance traveled during the first 6 seconds.(f) Draw a diagram like Figure 2 to illustrate the motion of the particle.(g) Find the acceleration at time $t$ and after 1 second.(h) Graph the position, velocity, and acceleration functions for $0 \le t \le 6.$(i) When is the particle speeding up? When is it slowing down?$f(t) = t^2 e^{-t}$

## a) $v=t e^{-t}(2-t)$b) $v \approx 0.368 \mathrm{ft} / \mathrm{s}$c) $t=0 \mathrm{s}$ and $t=2 \mathrm{s}$d) see solutione) see solutionf) graph unavailableg) $a=\left(t^{2}-4 t+2\right) e^{-t}$ and $a=-0.368 \mathrm{ft} / \mathrm{s}^{2}$h) see solutioni) see solution

Derivatives

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Oregon State University

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Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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