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
Kipish [7]
3 years ago
15

The position of a particle moving along the x axis varies in time according to the expression x = 4t 2, where x is in meters and

t is in seconds. Evaluate its position at the following times.
(a)t=2.10s
______m

(b)t=2.10s +Δt
xf=________m

(c)Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.10 s.
_______m/s ...?
Physics
2 answers:
Pie3 years ago
8 0

Answer:

a) X = 17.64 m

b) X = 17.64 + 4∆t^2 + 16.8∆t

c) Velocity = lim(∆t→0)⁡〖∆X/∆t〗 = 16.8 m/s

Explanation:

a) The position at t = 2.10s is:  

                 X = 4t^2

                 X = 4(2.10)^2

                 X = 17.64 m

b) The position at t = 2.10 + ∆t s  will be:

                 X = 4(2.10 + ∆t)^2

                 X = 17.64 + 4∆t^2 + 16.8∆t  m

c) ∆X is the difference between position at t = 2.10s and t = 2.10 + ∆t so,

                 ∆X= 4∆t^2 + 16.8∆t

Divide by ∆t on both sides:  

                ∆X/∆t =  4∆t + 16.8

 Taking the limit as ∆t approaches to zero we get:  

              Velocity =lim(∆t→0)⁡〖∆X/∆t〗 = 4(0) + 16.8

              Velocity = 16.8 m/s

 

zzz [600]3 years ago
3 0
R:  <span>For b) you just need to plug in "3.5 + Δt" as "t" in the formula for x, and simplify: 

x = 2(3.5 + Δt)^2 
x = 2(12.25 + 7Δt + Δt^2) 
x = 2Δt^2 + 14Δt + 24.5 

For c) we need to figure out what Δx is; presumably Δx is the difference in position between t = 3.5 and t = 3.5 + Δt. In other words, Δx = 2Δt^2 + 14Δt. 

So Δx/Δt is therefore 2Δt + 14. The limit of this as Δt approaches zero is 14, so the velocity is 14 at t = 3.5. 

We can check this by taking the derivative of x with respect to t: 

dx/dt = 4t 

So at t = 3.5, dx/dt (or velocity) is equal to 14, which matches what we came up with above using the limit.</span>
You might be interested in
A bag of cement has a mass of 62 g. What is the mass of the bag of cement in S.I. units (kg)?
NNADVOKAT [17]

The mass of this bag of cement in S.I. units (kg) is equal to 0.062 kilograms.

<u>Given the following data:</u>

  • Mass of cement = 62 grams.

To calculate the mass of this bag of cement in S.I. units (kg):

<h3>How to convert to S.I. units.</h3>

In Science, kilograms (kg) is the standard unit of measurement or S.I. units of the mass of a physical object. Thus, we would convert the value of the mass of this bag of cement in grams to kilograms (kg) as follows:

<u>Conversion:</u>

1000 grams = 1 kilograms.

62 grams = X kilograms.

Cross-multiplying, we have:

X = \frac{62}{1000}

X = 0.062 kilograms.

Read more on mass here: brainly.com/question/13833323

8 0
2 years ago
MY LAST ONE&lt;,Brainliest for best answer!
grigory [225]
_Award brainliest if helped!
Mechanical Advantage = Force by Hammer / Force by Nail = 160/40 = 4
8 0
3 years ago
Read 2 more answers
Helium-4 has how many protons
Natalka [10]

Answer: Helium has 2 protons.

4 0
3 years ago
What type of rays would you expect to be used frequently at a hospital to make medical diagnoses?
Bess [88]
X rays because to see your bones
7 0
3 years ago
A batter swings at a baseball. The action force is the bat hitting the ball with a force of 5N. What is the reaction force?
omeli [17]
The ball hitting the bat
6 0
3 years ago
Read 2 more answers
Other questions:
  • A rocket is launched at the rate of 11 feet per second from a point on the ground 15 feet from an observer. to 2 decimal places
    9·2 answers
  • The wavelength of an electromagnetic waves is __________ also known as the period. the number of waves that pass a given point i
    9·1 answer
  • Compare and contrast an electric discharge with an electric current
    12·1 answer
  • The theory of light has been expounded differently by scientists in different periods of time. What is an important reason for t
    13·1 answer
  • A hot air balloon contains 85,000 moles of air. To what temperature must the
    8·1 answer
  • I know the enthalpy of a reaction is 23kj/mol. Initially the reaction is taking place at 273 k. To what temperature do i need to
    6·1 answer
  • To collect quantitative data, scientists use all of the following except _____.
    10·2 answers
  • If someone is driving 100 miles in 60 minutes then drives 150 miles in 100 minutes west, what is his acceleration rate.
    6·1 answer
  • Give proof that mass is constant and weight keeps changing.​
    8·1 answer
  • Develop a model (diagram) that shows how different amounts of gravitational potential energy (GPE) are stored in the earth-ball
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!