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A particle moves along the
x-axis with velocity

v(t)=ln(t^(2)+5t+1)". "
What is the particle's displacement between the times
t=1 and
t=5 ?
Use a graphing calculator and round your answer to three decimal places.

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 $t=1$ and $t=5$ ? $\newline$ 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

\newline

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

\newline

What is the particle's displacement between the times

t=1

and

t=5

?

\newline

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

Integrate Velocity Function: To find the displacement, we need to integrate the velocity function from $t=1$ to $t=5$ .
Set Up Integral: Set up the integral: $\int_{1}^{5} \ln(t^2 + 5t + 1) \, dt$ .
Evaluate Integral: Use a graphing calculator to evaluate the integral.
Calculate Displacement: After using the calculator, we get the approximate value of the integral, which is the displacement.
Approximate Displacement: The calculator shows the displacement is approximately $9.154$ .

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

\newline

The horizontal displacement,

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, initial velocity,

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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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seconds after he started riding.

\newline

What is the best interpretation for the following statement?

\newline

The value of the derivative of

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\newline

1

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A) During the first

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5

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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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t=7

\newline

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

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Question

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

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\newline

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

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Question

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

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Question

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

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P=m v)

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Question

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

\newline

4

\newline

5

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7

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

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and her balance at the end of three years,

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r

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\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}

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Question

10\text{-kg}

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14\, \text{m}

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