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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?$f(t) = \sin (\pi t/2)$

## a) $\frac{5}{2} \cos (\pi t / 2)(\text { in } \mathrm{ft} / \mathrm{s})$b) $0 \mathrm{ft} / \mathrm{s}$c) $t=1+2 n$d) $(0,1),(3,5),(5,7)$ and so one) 6 feetf) graph unavailableg) $a=-\frac{\pi^{2}}{4} \sin \left(\frac{\pi t}{2}\right)$ and $a \approx-2.47 \mathrm{ft} / \mathrm{s}^{2}$h) graph unavailablei) $1+2 n \pi<t<2+2 n \pi$$\mathrm{OR} :$$3+2 n \pi<t<4+2 n \pi$

Derivatives

Differentiation

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Missouri State University

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University of Michigan - Ann Arbor

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Idaho State University

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Oregon State University

#### Topics

Derivatives

Differentiation

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp