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
Can you help me with this worksheet
ser-zykov [4K]
1. Vertical
2. Adjacent
3. Complementary
4. 72
5. X= 33
3 0
3 years ago
Read 2 more answers
Please help me branniest
weeeeeb [17]

Answer:

the answer is a


8 0
3 years ago
Two numbers are in the ratio 3:2, if the smaller number is 10. what is the bigger number?
boyakko [2]

Answer:

Step-by-step explanation:

I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me..

3 0
3 years ago
HELP PLEASEEE!!!! I START SCHOOL TOMORROW
ohaa [14]

Answer:

4. The range is -2 ≤ y ≤ 4

5. The domain is {-2 , -1 , 0 , 3.5 , 4.2}

6. The relation is not a function

Step-by-step explanation:

* Lets explain how to solve the problem

# Question 4:

- The range of the function is the values of all y (output) which is

 corresponding to the values of all x (input)

- The figure is a stare, the values of x is from -4 to 4

∴ The domain is -4 ≤ x ≤ 4

- The corresponding values of y are from -2 to 4

∴The range is -2 ≤ y ≤ 4

# Question 5:

- The table represent a relation between x and y

- x is the input of the relation

- y is the output of the relation

∵ The input of the relation is called the domain of it

∴ The domain of the relation is all values of x in the table

- the values of x are -2 , -1 , 0 , 3.5 , 4.2

∴ The domain is {-2 , -1 , 0 , 3.5 , 4.2}

# Question 6:

- The relation can be a function if each ordered pair has a

  unique value of x (input)

- That means every x (input) has only one y (output)

- Ex : The relation {(a , b) , (c , d) , (a , f)} is not a function because

 the input a has two output b and f

∵ The relation is {(-4 , 0) , (-3 , 0) , (-2 , 1) , (1 , -2) , (-3 , 4)}

∵ The x = -3 has two values of y 0 and 4

∴ The relation is not a function

7 0
3 years ago
Find the median of the following heights which are in inches. <br>62,72,83,61,60,70,67,68,68,68
krok68 [10]
The answer is 68 because is repeating 3 times
7 0
3 years ago
Other questions:
  • A refreshment stand makes 2 large servings of frozen yogurt from 3 pints. Add the line to the graph and write the equation.
    9·2 answers
  • Given the following set of data: 3, 4, 5, 6, 8, 9, 9, which measures below have a value of 6? (Check all that apply.)
    15·1 answer
  • What is 17.318 rounded to the nearest hundreth
    10·1 answer
  • Consider the original rectangle and the rectangle that has been reduced by 0.5.
    11·1 answer
  • -8 (1+11a)?????????????????
    6·2 answers
  • Answer the question
    14·1 answer
  • In the space below, identify the rate of change using the statement: The rate of change is
    11·2 answers
  • Give the slope-intercept form of the equation of the line that is perpendicular to –7x – 8y = 12 and contains P(–3, 1)
    9·1 answer
  • A company rents movies that can be streamed online or downloaded to a computer. The company charges a one-time sign-up fee and a
    5·2 answers
  • Please Help Will Mark Brainly
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!