Answer:
1) 50 seconds 2) 100°C
Explanation:
(Follows formula of Power=Energy/Time)
1) 500W x X = 2000J/kg°C x .25kg x 50°C
X = 50 seconds.
2) 2000W x 300s = 1000J/kg°C x 2kg x X
X = 300
Initial temperature => 400°C-300°C = 100°C
We are given: Final velocity (
)=20 m/s .
Time t= 2.51 s and
distance s = 82.9 m.
We know, equation of motion

Let us plug values of final velocity, and time in above equation.


Subtracting 2.51a from both sides, we get
-----------equation(1)
Using another equation of motion

Plugging values of vi =20-2.51a, t=2.51 and distnace s=82.9 in this equation.
We get,

Now, we need to solve it for a.
20-20+2.51a=165.8a.
-163.29a=0
a=0.
So, the acceleration would be 0 m/s^2.
Answer: 1 m/s
Explanation:
We have an object whose position
is given by a vector, where the components X and Y are identified by the unit vectors
and
(where each unit vector is defined to have a magnitude of exactly one):
![r=[2 m + (2 m/s) t] i + [3 m - (1 m/s^{2})t^{2}] j](https://tex.z-dn.net/?f=r%3D%5B2%20m%20%2B%20%282%20m%2Fs%29%20t%5D%20i%20%2B%20%5B3%20m%20-%20%281%20m%2Fs%5E%7B2%7D%29t%5E%7B2%7D%5D%20j)
On the other hand, velocity is defined as the variation of the position in time:

This means we have to derive
:
![\frac{dr}{dt}=\frac{d}{dt}[2 m + (2 m/s) t] i + \frac{d}{dt}[3 m - (1 m/s^{2})t^{2}] j](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B2%20m%20%2B%20%282%20m%2Fs%29%20t%5D%20i%20%2B%20%5Cfrac%7Bd%7D%7Bdt%7D%5B3%20m%20-%20%281%20m%2Fs%5E%7B2%7D%29t%5E%7B2%7D%5D%20j)
This is the velocity vector
And when
the velocity vector is:

This is the velocity vector at 2 seconds
However, the solution is not complete yet, we have to find the module of this velocity vector, which is the speed
:


Finally:
This is the speed of the object at 2 seconds
Answer:
a) 0.0625 I_1
b) 3.16 m
Explanation:
<u>Concepts and Principles </u>
The intensity at a distance r from a point source that emits waves of power P is given as:
I=P/4π*r^2 (1)
<u>Given Data</u>
f (frequency of the tuning fork) = 250 Hz
I_1 is the intensity at the source a distance r_1 = I m from the source.
<u>Required Data</u>
- In part (a), we are asked to determine the intensity I_2 a distance r_2 = 4 in from the source.
- In part (b), we are asked to determine the distance from the tuning fork at which the intensity is a tenth of the intensity at the source.
<u>solution:</u>
(a)
According to Equation (1), the intensity a distance r is inversely proportional to the distance from the source squared:
I∝1/r^2
Set the proportionality:
I_1/I_2=(r_2/r_1)^2 (2)
Solve for I_2 :
I_2=I_1(r_2/r_1)^2
I_2=0.0625 I_1
(b)
Solve Equation (2) for r_2:
r_2=(√I_1/I_2)*r_1
where I_2 = (1/10)*I_1:
r_2=(√I_1/1/10*I_1)*r_1
=3.16 m
Answer:
The moon region
Explanation:
This is because there is little to no gravity on the moon. That is where the astronaut would feel the lightest.