A mass M subway train initially traveling at speed v slows to a stop in a station and then stays there long enough for its brakes to cool. The station's volume is V and the air in the station has a density rho_air and specific heat C_air.
Assuming all the work done by the brakes in stopping the train is transferred as heat uniformly to all the air in the station, what is the expression for the change in the air temperature in the station? Make sure the quantities you enter match the ones given in the problem exactly.

Complete Question

The complete question is shown on the first uploaded image  

The expression for the change in the air temperature is  

Explanation:

From the question we are told  that

     The mass of the train is  M

     The speed of the train is  v

     The volume of the station is  V

      The density of air in the station is  

       The specific heat of air is  

The workdone by the break can be mathematically represented as

Now this is equivalent to the heat  transferred to air in the station

   Now the heat capacity of the air in the station is mathematically represented as

Now Since this is equivalent to the workdone by the breaks we have that

=>    

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.