Answer and Explanation:
Data provided in the question
Carbon mass = m
Initial speed = v_i
Coefficient = μk
Based on the above information, the expressions are as follows
a. By using the energy considerations the expression for the carton moving distance is
As we know that

where,





b. The initial speed of the carton if the factor of 3 risen, so the expression is




The final atmospheric pressure is 
Explanation:
Assuming that the temperature of the air does not change, we can use Boyle's law, which states that for a gas kept at constant temperature, the pressure of the gas is inversely proportional to its volume. In formula,

where
p is the gas pressure
V is the volume
The equation can also be rewritten as

where in our problem we have:
is the initial pressure (the atmospheric pressure at sea level)
is the initial volume
is the final pressure
is the final volume
Solving the equation for p2, we find the final pressure:

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Answer:
Option D.
Value cannot be calculated without knowing the speed of the train
Explanation:
The speed of the beam can only be calculated accurately when the speed of the train is put into consideration. Based of the theory of relativity, the observer is on the ground, and the train is moving with the beam of light inside it. This causes a variation in the reference frames when making judgements of the speed of the beam. The speed of the beam will be more accurate if the observer is moving at the same sped of the train, or the train is stationary.
To get the correct answer, we have to subtract the speed of the train from the speed calculated.
Answer:
The speed of space station floor is 49.49 m/s.
Explanation:
Given that,
Mass of astronaut = 56 kg
Radius = 250 m
We need to calculate the speed of space station floor
Using centripetal force and newton's second law




Where, v = speed of space station floor
r = radius
g = acceleration due to gravity
Put the value into the formula


Hence, The speed of space station floor is 49.49 m/s.