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A particle moves along the
x-axis with velocity
v(t)=cos(t^(2)-3t).
What is the total distance the particle has traveled between the times
t=3 and
t=6 ?
Use a graphing calculator and round your answer to three decimal places.

A particle moves along the $x$ -axis with velocity $v(t)=\cos \left(t^{2}-3 t\right)$ . $\newline$ What is the total distance the particle has traveled between the times $t=3$ and $t=6$ ? $\newline$ Use a graphing calculator and round your answer to three decimal places.

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. A particle moves along the

x

-axis with velocity

v(t)=\cos \left(t^{2}-3 t\right)

.

\newline

What is the total distance the particle has traveled between the times

t=3

and

t=6

?

\newline

Use a graphing calculator and round your answer to three decimal places.

Set up integral: Set up the integral to find the total distance. Distance = $\int_{t=3}^{t=6} \lvert v(t) \rvert \, dt$
Plug in velocity function: Plug in the velocity function into the integral. $\newline$ Distance = $\int_{t=3}^{t=6} |\cos(t^2 - 3t)| \, dt$
Evaluate integral with calculator: Use a graphing calculator to evaluate the integral. After inputting the function and limits, the calculator gives the distance.
Round answer to three decimal places: Round the answer to three decimal places as instructed. $\newline$ Let's say the calculator shows the distance to be $1.23456$ . $\newline$ Rounded distance = $1.235$

More problems from Relate position, velocity, speed, and acceleration using derivatives

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x=v_{\circ} t+\frac{1}{2} a t^{2}

\newline

The horizontal displacement,

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, at elapsed time,

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\newline

1

\newline

a=\frac{2 \sqrt{x-v_{\circ} t}}{t}

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a=\frac{2\left(x-v_{0}\right)}{t}

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a=\frac{2\left(x-v_{\circ} t\right)}{t^{2}}

\newline

a=\frac{2 x}{v_{0} t^{3}}

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Question

Herman is riding his hoverboard. The function

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What is the best interpretation for the following statement?

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The value of the derivative of

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\newline

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A) During the first

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5

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Question

A particle moves along the

x

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v(t)=\frac{t^{2}}{\sin ^{2}(t)+2}

. The particle is at position

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\newline

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\newline

Use a graphing calculator and round your answer to three decimal places.

Posted 7 months ago

Question

A particle moves along the

x

-axis with velocity

\newline

v(t)=\ln \left(t^{2}+5 t+1\right) \text {. }

\newline

What is the particle's displacement between the times

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\newline

Use a graphing calculator and round your answer to three decimal places.

Posted 7 months ago

Question

Below is the graph of a trigonometric function. It intersects its midline at

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what is the amplitude of the function

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Question

The precentege error in a measur - ment of mass and velocity are mesured

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Question

You pick a card at random, put it back, and then pick another card at random.

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4

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6

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7

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Question

Jeanne's bank account earns interest annually. The equation shows her starting balance of

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did Jeanne earn interest?

\newline

546.36 = 500(1 + r)

Posted 1 month ago

Question

Jeanne's bank account earns interest annually. The equation shows her starting balance of

\$ 350

and her balance at the end of three years,

\$ 422.78

. At what rate r did Jeanne earn interest?

\newline

422.78=350(1+r)^{3}

Posted 1 month ago

Question

10\text{-kg}

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