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Tom [10]
3 years ago
8

A particle moves along a line with acceleration a (t) = -1/(t+2)2 ft/sec2. Find the distance traveled by the particle during the

time interval [0, 5], given that the initial velocity v(0) is 1/2 ft/sec. -4 1n(2)+4 1n(7)ft -ln(2)+ln(7)ft -31n(2) + 31n(7) ft -21n(2) + 21n(7) ft -1/2 ln(2) + 1/2ln(7)ft
Mathematics
1 answer:
amm18123 years ago
3 0

Answer:

s(t)=(ln|7|+ln|2|)\,ft

Step-by-step explanation:

Acceleration is second derivative of distance and are related as:

a(t)=\frac{d^2s}{dt^2}\\\\\frac{d^2s}{dt^2}=\frac{-1}{(t+2)^2}\\

Integrating both sides w.r.to t

v(t)=\frac{ds}{dt}=\frac{1}{t+2} +C\\

Using initial value

v(0)=\frac{1}{2}\\\\\frac{1}{2}=\frac{1}{0+2} +C\\\\C=0\\\\\frac{ds}{dt}=\frac{1}{t+2}

We have to calculate the distance covered in time interval [0,5], so:

\int\limits^5_0 \frac{ds}{dt}=\int\limits^5_0 {\frac{1}{t+2}} \, dt\\\\s(t)=[ln|t+2|]^5_0\\\\s(t)=ln|5+2|+ln|0+2|\\\\s(t)=(ln|7|+ln|2|)\,ft

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<h3>What is trigonometry?</h3>

Your information is incomplete as the triangles aren't given. Therefore, an overview will be given.

It should be noted that trigonometry simply means the branch of mathematics that is concerned with angles and their application to calculation.

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2 years ago
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Goshia [24]

Answer:

see explanation

Step-by-step explanation:

Given

2BD = 7BT , then

2(d - b ) = 7(t - b) ← distribute both sides

2d - 2b = 7t - 7b ( add 7b to both sides )

2d + 5b = 7t, thus

2\left[\begin{array}{ccc}10.5\\10\\\end{array}\right] + 5\left[\begin{array}{ccc}0\\3\\\end{array}\right] = 7t

\left[\begin{array}{ccc}21\\20\\\end{array}\right] + \left[\begin{array}{ccc}0\\15\\\end{array}\right] = 7t

\left[\begin{array}{ccc}21\\35\\\end{array}\right] = 7t , thus

t = \frac{1}{7}\left[\begin{array}{ccc}21\\35\\\end{array}\right] = \left[\begin{array}{ccc}3\\5\\\end{array}\right]

Hence T = (3, 5 )

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2 years ago
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gavmur [86]

Answer:

da baby

Step-by-step explanation:

covirtible

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3 years ago
A giraffe can run about 14 meters per second. Find it's speed in miles per hour
Inga [223]
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drek231 [11]

Answer:

answer is (3,7)

Step-by-step explanation:

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