Answer:
<u><em>note:</em></u>
<u><em>solution is attached due to error in mathematical equation. please find the attachment</em></u>
Answer:

Explanation:
<u>Work and Kinetic Energy
</u>
The work an object does due to its motion is equal to the change of its kinetic energy. Being ko and k1 the initial and final kinetic energy respectively and m the mass of the object, then

Since

We have

The truck has a mass of 60,000 kg and is moving at 27 m/s. The runaway truck ramp must stop the truck, so the final speed is 0. Thus



Answer:
a) 3.39 × 10²³ atoms
b) 6.04 × 10⁻²¹ J
c) 1349.35 m/s
Explanation:
Given:
Diameter of the balloon, d = 29.6 cm = 0.296 m
Temperature, T = 19.0° C = 19 + 273 = 292 K
Pressure, P = 1.00 atm = 1.013 × 10⁵ Pa
Volume of the balloon = 
or
Volume of the balloon = 
or
Volume of the balloon, V = 0.0135 m³
Now,
From the relation,
PV = nRT
where,
n is the number of moles
R is the ideal gas constant = 8.314 kg⋅m²/s²⋅K⋅mol
on substituting the respective values, we get
1.013 × 10⁵ × 0.0135 = n × 8.314 × 292
or
n = 0.563
1 mol = 6.022 × 10²³ atoms
Thus,
0.563 moles will have = 0.563 × 6.022 × 10²³ atoms = 3.39 × 10²³ atoms
b) Average kinetic energy = 
where,
Boltzmann constant,
Average kinetic energy = 
or
Average kinetic energy = 6.04 × 10⁻²¹ J
c) rms speed = 
where, m is the molar mass of the Helium = 0.004 Kg
or
rms speed = 
or
rms speed = 1349.35 m/s
Answer:
This is known as a Galilean transformation where
V' = V - U
Where the primed frame is the Earth frame and the unprimed frame is the frame moving with respect to the moving frame
V - speed of object in the unprimed frame
U - speed of primed frame with respect to the unprimed frame
Here we have:
V = -15 m/s speed of ball in the moving frame (the truck)
U = -20 m/s speed of primed (rest) frame with respect to moving frame
So V' = -15 - (-20) = 5 m/s
It may help if you draw a vector representing the moving frame and then add
a vector representing the speed of the ball in the moving frame.
If time is specified, the distance may be estimated in constant acceleration using the formula: X=(at2)/2 if the beginning velocity is 0. (A automobile begins from a stop...) As a result, X=(6*10*10)/2=600/2 = 300 m.