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
vlada-n [284]
3 years ago
14

Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 1

4t i + sin t j + cos 2t k, v(0) = i, r(0) = j
Physics
1 answer:
kondor19780726 [428]3 years ago
4 0

Answer:

Explanation:

Given

Acceleration a(t)=14t\hat{i]+\sin (t)\hat{j}+\cos (2t)\hat{k}[/tex]

and v(0)=\hat{i}

r(0)=\hat{j}

we know a=\frac{\mathrm{d} v}{\mathrm{d} t}

\int dv=\int adt

v(t)=\int (14t\hat{i}+\sin (t)\hat{j}+\cos (2t)\hat{k})dt

v(t)=7t^2\hat{i}-\cos t\hat{j}+\frac{\sin (2t)\hat{k}}{2}+c

at t=0

v(0)=0-1\cdot \hat{j}+0+c

c=\hat{i}+\hat{j}

v(t)=(7t^2+1)\hat{i}+(1-\cos t)\hat{j}+\frac{\sin (2t)\hat{k}}{2}

and \frac{\mathrm{d} r}{\mathrm{d} t}=v(t)

\int dr=\int vdt

r(t)=\int ((7t^2+1)\hat{i}+(1-\cos t)\hat{j}+\frac{\sin (2t)\hat{k}}{2})dt

r(t)=(\frac{7}{2}t^3+t)\hat{i}+(t-\sin (t))\hat{j}+\frac{1}{2}\times (-\frac{1}{2}\cos 2t)\hat{k}+c_2

at t=0

r(0)=\hat{j}

r(t)=(\frac{7}{3}t^3+t)\hat{i}+(1+t-\sin t)\hat{j}+\frac{1}{4}(1-\cos 2t)\hat{k}

       

You might be interested in
What are the characteristics of an ideal transformer ​
Vsevolod [243]

It is an imaginary transformer which has no core loss, no ohmic resistance and no leakage flux. The ideal transformer has the following important characteristic. The resistance of their primary and secondary winding becomes zero. The core of the ideal transformer has infinite permeability.

4 0
3 years ago
An air compressor compresses 6 L of air at 120 kPa and 22°C to 1000 kPa and 400°C. Determine the flow work, in kJ/kg, required b
Mariana [72]

Answer:

The work flow required by the compressor = 100.67Kj/kg

Explanation:

The solution to this question is obtained from the energy balance where the initial and final specific internal energies and enthalpies are taken from A-17 table from the given temperatures using interpolation .

The work flow can be determined using the equation:

M1h1 + W = Mh2

U1 + P1alph1 + ◇U + Workflow = U2 + P2alpha2

Workflow = P2alpha2 - P1alpha1

Workflow = (h2 -U2) - (h1 - U1)

Workflow = ( 684.344 - 491.153) - ( 322.483 - 229.964)

Workflow = ( 193.191 - 92.519)Kj/kg

Workflow = 100.672Kj/kg

6 0
3 years ago
Technician A says that a tire will increase or decrease approximately 1 psi for each 10°F change of temperature. Technician B sa
bearhunter [10]

Answer:

Technician A

Explanation:

It is seen that a tire pressure will increase or decrease 1 psi for each 10^{\circ} F  change in temperature.

For Technician B vehicle pressure should not be adjusted after tire has been warmed as the warm air may increase the pressure but it will be auto adjusted as  the temperature falls to normal .          

8 0
3 years ago
Ax = 4.3 m
Dimas [21]

Answer:

the answer will be option no b plss mark me brainliest

7 0
3 years ago
A cohesive force between the liquids molecules is responsible for the fluids is called​
kiruha [24]

Answer:

static force

Explanation:

mark me brainliest

5 0
3 years ago
Read 2 more answers
Other questions:
  • Assume four 1 kohm resistors are connected so that they form a square. what is the equivalent resistance if the resistance is me
    14·1 answer
  • Ocean currents near the equator are primarily: eastward westward north and south clockwise
    13·1 answer
  • A 2.16 x 10-2-kg block is resting on a horizontal frictionless surface and is attached to a horizontal spring whose spring const
    12·1 answer
  • Why is dark silicon currently necessary?
    12·1 answer
  • Does a neutrally charged object even have a charge?
    8·2 answers
  • In addition to a reference point you also need distance and __________ to describe location
    8·1 answer
  • SCIENCE
    6·2 answers
  • A solid sphere of radius R, a solid cylinder of radius R, and a rod of length R all have the same mass, and all three are rotati
    12·1 answer
  • Violet light has a frequency of 7.26 × 1014 Hz and travels at a speed of 3.00 × 108 m/s.
    8·1 answer
  • 234 oz to tons using the table method (US)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!