1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zmey [24]
3 years ago
12

The position equation for a particle is s of t equals the square root of the quantity t cubed plus 1 where s is measured in feet

and t is measured in seconds. Find the acceleration of the particle at 2 seconds.
1 ft/sec2
two thirds ft/sec2
negative 1 over 108 ft/sec2
None of these
Mathematics
2 answers:
vladimir1956 [14]3 years ago
8 0
\bf s(t)=\sqrt{t^3+1}
\\\\\\
\cfrac{ds}{dt}=\cfrac{1}{2}(t^3+1)^{-\frac{1}{2}}\cdot 3t^2\implies \boxed{\cfrac{ds}{dt}=\cfrac{3t^2}{2\sqrt{t^3+1}}}\leftarrow v(t)
\\\\\\
\cfrac{d^2s}{dt^2}=\cfrac{6t(2\sqrt{t^3+1})-3t^2\left( \frac{3t^2}{\sqrt{t^3+1}} \right)}{(2\sqrt{t^3+1})^2}\implies 
\cfrac{d^2s}{dt^2}=\cfrac{ \frac{6t(2\sqrt{t^3+1})-1}{\sqrt{t^3+1}} }{4(t^3+1)}

\bf \cfrac{d^2s}{dt^2}=\cfrac{6t[2(t^3+1)]-1}{4(t^3+1)\sqrt{t^3+1}}\implies 
\boxed{\cfrac{d^2s}{dt^2}=\cfrac{12t^4+12t-1}{4t^3+4\sqrt{t^3+1}}}\leftarrow a(t)\\\\
-------------------------------\\\\a(2)=\cfrac{215~ft^2}{44~sec}
Eva8 [605]3 years ago
7 0

Answer:

Acceleration of the particle is two thirds ft/s².

Step-by-step explanation:

It is given that, the position of the particle at time t is given by :

s(t)=\sqrt{t^3+1}

Where

s is in feet

t is in seconds

We need to find the acceleration of the particle at 2 seconds. Firstly calculating the velocity of the particle as :

v=\dfrac{ds(t)}{dt}

v=\dfrac{d(\sqrt{t^3+1})}{dt}    

This gives, v=\dfrac{3t^2}{2\sqrt{t^3+1}}

Since, a=\dfrac{dv}{dt}

a=\dfrac{d(\dfrac{3t^2}{2\sqrt{t^3+1}})}{dt}

a=\dfrac{3t^4+12t}{4(t^3+1)^{3/2}}

At t = 2 seconds,

a=\dfrac{3(2)^4+12(2)}{4((2)^3+1)^{3/2}}

a=0.66\ ft/s^2

or

a=\dfrac{2}{3}\ ft/s^2

So, the acceleration of the particle at 2 seconds is 2/3 ft/s². Hence, this is the required solution.

You might be interested in
Solve for x. 7^8=7^8×7^x
denis-greek [22]

Answer:

x = 0

Step-by-step explanation:

Apply the exponent rule.

7^8=7^{x+8} \\

If a^{f(x)} = a^{g(x)}  then f(x) = g(x)

8 = x + 8

x = 0

3 0
2 years ago
Solve equation please!! :) 10 points
dimulka [17.4K]
3(x-3)-15 = 0
3(x-3) = 15
3x-9 = 15
3x = 24
x = 8
3 0
2 years ago
Read 2 more answers
What is the least common multiple of 31, 28, and 14?
WINSTONCH [101]

<u>⇨ By prime factorization method:</u>

\begin{array}{r | l}{\sf{2 & {\sf14,28,31} \\\cline{2-2} {\sf2 & {\sf7,14,31 \\\cline{2-2} {\sf7 & {\sf7,7,31 \\\cline{2-2} {\sf31 & {\sf1,1,31 \\\cline{2-2} & {\sf1,1,1\end{array}

{\sf{LCM\: = \:2 \:x\: 2 \:x\: 7 \:x\: 31}}\\\\{\sf{LCM \:= \:868}}\\}\\{\sf{Therefore,}}\\\\{\sf{LCM\:(14,\: 28,\: 31)\: = \:868

{\boxed{\sf{LCM\:=\:868}}

5 0
2 years ago
Assume the probability is one half that a child born is a girl. if a family has three​ children, what is the probability that th
arsen [322]

1/3 chances that it will be a girl or a boy because their is only a 50/50% and their is 3 children


3 0
2 years ago
in comparing the galilean transformations with the lorentz transformations, what multiplicative factor appears in the lorentz tr
raketka [301]

In Lorentz transformations we have velocity based factors that is not present in Galilean ones.

<h3>What is lorentz transformations?</h3>

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch physicist Hendrik Lorentz is credited with coining the name of the transformation. There are two frames of reference: Inertial Frames, which refer to motion that has a constant speed.

<h3>What are Galilean transformations?</h3>

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch scientist Hendrik Lorentz is credited with coining the term transformation. There are two frames of reference: Inertial Frames, which relate to motion that has a constant speed.

Any and all rulers and other self-contained length standards, such as those you might use to set up a measurement frame, can be contracted in length based on velocity. This results in the Lorentz factor at the place in the LT.

Any and all clocks and other physically independent systems, such as those used to record events in a measurement frame, are subject to velocity time dilation. As a result, the LF is temporarily in the LT.

The fact that applying Einstein synchronisation individually for each measurement frame turns out to be natural. Consequently, the position-dependent synchronisation offset between the clocks of one measurement frame and those of the other is represented by the enigmatic second term in the LT for the time.

To learn more about transformations click the following link :-

brainly.com/question/1548871

#SPJ4

7 0
11 months ago
Other questions:
  • Today, Noah swam 1 mile at swim practice and Liam sprinted 880 yards at track practice. How many more yards did Noah travel duri
    14·1 answer
  • Phil baked two kinds of pie. Each pie pan was the same size. He served 1/2 of the blueberry pie. He served 1/4 of the apple pie.
    9·2 answers
  • A random sample of 49 measurements from one population had a sample mean of 15, with sample standard deviation 5. An independent
    6·1 answer
  • True or false
    5·2 answers
  • -[tex]-8\9 + 1/5+ -8/15
    10·1 answer
  • I have a few questions! what is the gcf for
    11·1 answer
  • If the original quantity is 10 and the new quantity is 15​, what is the percent​ increase?
    15·2 answers
  • Mrs. Lopez is designing her garden in the shape of a rectangle. The area of her garden is 2 times greater than the area of the r
    15·1 answer
  • Simplify (8) ÷ (2x3)
    11·1 answer
  • A can of paint is created by mixing 8oz of blue paint and 6 oz of red paint. If someone uses 24 oz of blue paint, then how many
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!