Answer:
let the speed of Allegra be x mph, then speed of Elliana is x+4 mph,
time to cover distance for Eliana is 2 hours, time to cover distance for Allegrais 2.5 hours,
since they both cover the same distance you have this,
distance (of Eliana) = distance (of Allegrais ),
distance=speed x time, so we have
speed (of Eliana) x time (of Eliana) = speed (of Allegra) x time (of Allegra),
2(x+4)=2.5x,
solve for x, then substitute back for speeds for Eliana and Allegra,
Eliana's speed = 16 + 4 = 20.
Allegra's speed = 16
Answer:
a)
, b) 
Explanation:
The magnitude of torque is a form of moment, that is, a product of force and lever arm (distance), and force is the product of mass and acceleration for rotating systems with constant mass. That is:



Where
is the angular acceleration, which is constant as torque is constant. Angular deceleration experimented by the unpowered flywheel is:


Now, angular velocities of the unpowered flywheel at 50 seconds and 100 seconds are, respectively:
a) t = 50 s.


b) t = 100 s.
Given that friction is of reactive nature. Frictional torque works on the unpowered flywheel until angular velocity is reduced to zero, whose instant is:


Since
, then the angular velocity is equal to zero. Therefore:

Answer:
-Increase in temperature: increase
-Decrease in temperature: decrease
-Increase in volume: increase
-Decrease in volume: decrease
-Increase in pressure: increase
-Decrease in pressure: decrease
Explanation:
-Increase in temperature:
● Molecules gain kinetic energy and move fast thus increasing distance
-Decrease in temperature:
● Kinetic energy of molecules decrease so they have smaller distance
-Increase in volume:
● Molecules have more space to move around so distance increase
-Decrease in volume:
● Less space, molecules collide with each other because of decreased distance thus increasing pressure
-Increase in pressure
● Molecules collide with each other and the walls of container increasing pressure so molecules move faster and it increases distance
-Decrease in pressure:
● Molecules collide with each other and walls of container less frequently so distance between molecules decrease
Answer:
d = 2.54 [m]
Explanation:
Through the theorem of work and energy conservation, we can find the work that is done. Considering that the energy in the initial state is only kinetic energy, while the energy in the final state is also kinetic, however, this is zero since the body stops.

where:
W = work [J]
Ek1 = kinetic energy at initial state [J]
Ek2 = kinetic energy at the final state = 0.
We must remember that kinetic energy can be calculated by means of the following expression.
![\frac{1}{2} *m*v^{2}-W=0\\W= \frac{1}{2} *4*(5)^{2}\\W= 50 [J]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D-W%3D0%5C%5CW%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A4%2A%285%29%5E%7B2%7D%5C%5CW%3D%2050%20%5BJ%5D)
We know that work is defined as the product of force by distance.

where:
F = force [N]
d = distance [m]
But the friction force is equal to the product of the normal force (body weight) by the coefficient of friction.
![f=m*g*0.5\\f = 4*9.81*0.5\\f = 19.62 [N]](https://tex.z-dn.net/?f=f%3Dm%2Ag%2A0.5%5C%5Cf%20%3D%204%2A9.81%2A0.5%5C%5Cf%20%3D%2019.62%20%5BN%5D)
Now solving the equation for the work.
![d=W/F\\d = 50/19.62\\d = 2.54[m]](https://tex.z-dn.net/?f=d%3DW%2FF%5C%5Cd%20%3D%2050%2F19.62%5C%5Cd%20%3D%202.54%5Bm%5D)
V^2 = 700J/0.5*35kg
V = square root of 40
v = 6.324 m/s