Answer:
a)We know that acceleration a=dv/dt
So dv/dt=kt^2
dv=kt^2dt
Integrating we get
v(t)=kt^3/3+C
Puttin t=0
-8=C
Putting t=2
8=8k/3-8
k=48/8
k=6
Answer:
vec(a) = 16 i + 16 j
mag(a) = 22.63 ft/s^2
Explanation:
Given,
- The two components of velocity are given for fluid flow:
u = 4*y ft/s
v = 4*x ft/s
Find:
What is the time rate of change of the velocity vector V (i.e., the acceleration vector) for a fluid particle at x = 1 ft. and y = 1 ft. at time t = 1 second?
Solution:
- The rate of change of velocity is given to be acceleration. We will take derivative of each components of velocity with respect to time t:
a_x = du / dt
a_x = 4*dy/dt
a_y = dv/dt
a_y = 4*dx/dt
- The expressions dx/dt is the velocity component u and dy/dt is the velocity component v:
a_x = 4*(4*y) = 16y
a_y = 4*(4*x) = 16x
- The acceleration vector can be expressed by:
vec(a) = 16y i + 16x j
- Evaluate vector (a) at x = 1 and y = 1:
vec(a) = 16*1 i + 16*1 j = 16 i + 16 j
- The magnitude of acceleration is given by:
mag(a) = sqrt ( a^2_x + a^2_y )
mag(a) = sqrt ( 16^2 + 16^2 )
mag(a) = 22.63 ft/s^2
Answer:
a) 
b) The flow would be going from section (b) to section (a)
Explanation:
1) Notation
For above conversions we use the conversion factor 
head loss from section
2) Formulas and definitions
For this case we can apply the Bernoulli equation between the sections given (a) and (b). Is important to remember that this equation allows en energy balance since represent the sum of all the energies in a fluid, and this sum need to be constant at any point selected.
The formula is given by:
Since we have a constant section on the piple we have the same area and flow, then the velocities at point (a) and (b) would be the same, and we have just this expression:
3)Part a
And on this case we have all the values in order to replace and solve for 
4)Part b
Analyzing the value obtained for 
is a negative value, so on this case this means that the flow would be going from section (b) to section (a).
· Branch circuits divide the main electrical service into separate pathways to feed electricity throughout the home. ... be either 120-volt circuits—which feed all the standard outlets and lighting circuits
