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
Chad bought 8 pounds of strawberries for 25.52. What is the cost, C, of 1 pound of strawberries
Bumek [7]
I think it would be 3.19.
Dividing 25.52 by 8.
5 0
3 years ago
Abdul has 15 shirts to fold. Let n be the number of shirts he would have left to fold after folding f of them. Write an equation
andrew-mc [135]

Answer:

n + f = 15

Step-by-step explanation:

n + f = 15

n + (6) = 15

n = 15 - 6 (opposite side opposite sign)

n = 9

4 0
2 years ago
Estelle treated her sister to lunch while visiting her in Lowell. Their lunch cost $80, and the sales tax in Lowell is 15%. If E
yan [13]

Answer:

Estelle paid $104 in total.

Step-by-step explanation:

15% of $80.00 is 12. So add 12 two times to 80 because of 15% sales tax and 15% tip.

3 0
3 years ago
Someone please help me with d.
Sav [38]
X=0.2
All you have to do is simplify both sides of the equation. Add 3x to both sides. Then subtract 0.8 from both sides.
8 0
3 years ago
Read 2 more answers
Assume a program has the following variable defenition: int a, b =2; float c = 4.2; and the following statement: a = b * c; What
Vladimir [108]

Answer:

The correct option is B.

Step-by-step explanation:

In a program the variables are defined as

int a, b =2;

float c = 4.2;

The given statement is

a = b * c

a = 2 * 4.2

a = 8.4

It is given that variable a is an integer. So, only integer value can be stored in a.

a ≈ 8

It means 8 will be stored in a. Therefore the correct option is B.

5 0
3 years ago
Other questions:
  • How do I find x and y?
    14·1 answer
  • What is the area of a circle with a diameter of 9.2 centimeters? Round your answer ro the nearest hundredth.
    8·1 answer
  • Which of the following statements are true for a trapezoid?
    12·2 answers
  • Write using exponents. Work from left to right on the grid. 7*7*7*7
    12·2 answers
  • Ibrahim has some building blocks that are all cubes of the same size. He uses three of the blocks to make a pile with a height o
    7·1 answer
  • Mrs Ross class has 24 students. 2/3 of her students have brown hair. The rest have blonde hair. How many students have brown hai
    14·2 answers
  • Solve the inequality -2x<16
    13·2 answers
  • Your friend says she used a common
    5·2 answers
  • 60 students want lemonade and 16 students want iced tea. What is the ratio of the number of students who want iced tea to the nu
    9·1 answer
  • PLease someone help with this, I've looked everywhere and can't get a solid answer to anything!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!