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lana [24]
3 years ago
12

A train is moving in a straight railway where it covered one third of the distance with

Physics
1 answer:
Alexxandr [17]3 years ago
5 0

Answer:

<em>The average speed of the train is 45 km/h</em>

Explanation:

<u>Speed</u>

It's defined as the distance (d) per unit of time (t) traveled by an object. The formula is:

\displaystyle v=\frac{d}{t}

Let's call x the total distance covered by the train. It covered d1=1/3x with a speed of v1=25 km/h. The time taken is calculated solving for t:

\displaystyle t_1=\frac{d_1}{v_1}

\displaystyle t_1=\frac{1/3x}{25}

\displaystyle t_1=\frac{x}{75}

Now the rest of the distance:

d2 = x - 1/3x = 2/3x

Was covered at v2=75 km/h. Thus the time taken is:

\displaystyle t_2=\frac{d_2}{v_2}

\displaystyle t_2=\frac{2/3x}{75}

\displaystyle t_2=\frac{2x}{225}

The total time is:

\displaystyle t_t=\frac{x}{75}+\frac{2x}{225}

\displaystyle t_t=\frac{3x}{225}+\frac{2x}{225}

\displaystyle t_t=\frac{5x}{225}

Simplifying:

\displaystyle t_t=\frac{x}{45}

The average speed is the total distance divided by the total time:

\displaystyle \bar v=\frac{x}{\frac{x}{45}}

Simplifying:

\boxed{\displaystyle \bar v=45\ km/h}

The average speed of the train is 45 km/h

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Potassium is a crucial element for the healthy operation of the human body. Potassium occurs naturally in our environment and thus our bodies) as three isotopes: Potassium-39, Potassium-40, and Potassium-41. Their current abundances are 93.26%, 0.012% and 6.728%. A typical human body contains about 3.0 grams of Potassium per kilogram of body mass. 1. How much Potassium-40 is present in a person with a mass of 80 kg? 2. If, on average, the decay of Potassium-40 results in 1.10 MeV of energy absorbed, determine the effective dose (in Sieverts) per year due to Potassium-40 in an 80- kg body. Assume an RBE of 1.2. The half-life of Potassium-40 is 1.28 * 10^9years.

Answer:

The potassium-40 present in 80 kg is  Z = 0.0288 *10^{-3}\ kg

The effective dose absorbed per year is  x = 2.06 *10^{-24} per year

Explanation:

From the question we are told that

      The mass of potassium in 1 kg of human body is m =  3g= \frac{3}{1000} =  3*10^{-3} \ kg

      The mass of the person is M = 80 \ kg

       The abundance of Potassium-39 is   93.26%

        The abundance of Potassium-40 is   0.012%

         The abundance of Potassium-41 is   6.78 %

         The energy absorbed is  E =  1.10MeV = 1.10 *10^{6} * 1.602 *10^{-19} = 1.7622*10^{-13} J

Now  1 kg of human body contains       3.0*10^{-3}\ kg of  Potassium

So      80 kg of human body contains      k kg of  Potassium

=>   k = \frac{ 80 * 3*10^{-3}}{1}

     k = 0.240\  kg

Now from the question potassium-40 is  0.012% of the total  potassium so

     Amount of potassium-40  present is mathematically represented as

            Z = \frac{0.012}{100}  * 0.240

            Z = 0.0288 *10^{-3}\ kg

The effective dose (in Sieverts) per year due to Potassium-40 in an 80- kg body is mathematically evaluated as

           D =  \frac{E}{M}

Substituting values

          D =  \frac{1.7622*10^{-13}}{80}

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Converting to Sieverts

We have

           D_s = REB * D

           D_s = 1.2 * 2.2 *10^{-15}

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     for half-life (1.28 *10^9 \ years)  the dose is  2.64 *10^{-15}

     Then for 1  year the dose would be  x

=>         x = \frac{2.64 *10^{-15}}{1.28 * 10^9}

             x = 2.06 *10^{-24} per year      

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