The acceleration of a particle is constant. At t = 0, the particle is at the origin and the velocity of the particle is vo = vji+ v2j. At time t = T, the velocity of the particle is v = v3j. Here v1, v2, and v3 are constants with dimensions of length divided by time. All answers should be written in terms of vj, v2, V3, T, and the unit vectors i and j. Part (a) What is the particle's acceleration vector?
Part (b) What is the particle's position vector at t= 2T?
Part (c) What is the particle's velocity vector at t =2T?

a) a = i ^ + j^, b) r = 2 v₃ T j ^, c)    v = -v₁ i ^ + (2 v₃ - v₂) j ^

Explanation:

This is a two-dimensional kinematics problem

a) Let's find the acceleration of the body, for this let's use a Cartesian coordinate system

X axis

initial velocity v₀ₓ = v₁ for t = 0, velocity reaches vₓ = 0 for t = T, let's use

          vₓ = v₀ₓ + aₓ t

we substitute

          for t = T

           0 = v₁ + aₓ T

           aₓ = - v₁ / T

y axis  

the initial velocity is = v₂ at t = 0 s, for time t = T s the velocity is v_{y} = v₃

             v₃ = v₂ + a_{y} T

              a_{y} =

therefore the acceleration vector is

             a = i ^ + j^

b) the position vector at t = 2T, we work on each axis

X axis

             x = v₀ₓ t + ½ aₓ t²

we substitute

             x = v₁ 2T + ½ (-v₁ / T) (2T)²

              x = 2v₁ T - 2 v₁ T

              x = 0

Y axis  

             y = t + ½ a_{y} t²

             y = v₂ 2T + ½ 4T²

             y = 2 v₂ T + 2 (v₃ -v₂) T

            y = 2 v₃ T

the position vector is

            r = 2 v₃ T j ^

c) the velocity vector for t = 2T

X axis

            vₓ = v₀ₓ + aₓ t

we substitute

           vₓ = v₁ - 2T = v₁ - 2 v₁

           vₓ = -v₁

Y axis  

            = v_{oy} + a_{y} t

           v_{y} = v₂ + 2T

           v_{y} = v₂ + 2 v₃ - 2v₂

           v_{y} = 2 v₃ - v₂

the velocity vector is

           v = -v₁ i ^ + (2 v₃ - v₂) j ^

nec chapter 5 contains

c. information on special occupancy areas

nec chapter 6 covers

a. special equipment

which of the following rules contain the words shall or shall not and must be adhered to?

b. mandatory rules

which of the following rules identify actions that are allowed but not required and typically cover options or alternative methods?

c. optional rules

which of the following serves as the introduction to the nec and provides an overview of the book?

a. nec article 90

organizations that test products for safety are

c. nrtls

the nec is published by the

a national fire protection association

the nec is divided into

b. 9 chapters

the nec provides informative annexes for

c. informational materials and examples

two terms from nec article 100 that trainees should become familiar with are

b. labeled and listed

explanation:

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz