Displacement is a vector magnitude that depends on the position of the body which is individualistic for the trajectory.
While, Distance is a scalar magnitude that measures over the trajectory.
Hi! The answer is ‘B’! Because the nucleus is found at the center and contains protons (positive charge) and neutrons (no charge)
Answer:
- The work made by the gas is 7475.69 joules
- The heat absorbed is 7475.69 joules
Explanation:
<h3>
Work</h3>
We know that the differential work made by the gas its defined as:
We can solve this by integration:
but, first, we need to find the dependence of Pressure with Volume. For this, we can use the ideal gas law
This give us
As n, R and T are constants
![\Delta W= \ n \ R \ T \left [ ln (V) \right ]^{v_2}_{v_1}](https://tex.z-dn.net/?f=%20%5CDelta%20W%3D%20%5C%20n%20%5C%20R%20%5C%20T%20%20%5Cleft%20%5B%20ln%20%28V%29%20%5Cright%20%5D%5E%7Bv_2%7D_%7Bv_1%7D%20)
But the volume is:
Now, lets use the value from the problem.
The temperature its:
The ideal gas constant:
So:
<h3>Heat</h3>
We know that, for an ideal gas, the energy is:
where 
its the internal energy of the gas. As the temperature its constant, we know that the gas must have the energy is constant.
By the first law of thermodynamics, we know
where 
is the Work made by the gas (please, be careful with this sign convention, its not always the same.)
So:
The equation of the car is given by the equation,
x(t) = 2.31 + 4.90t² - 0.10t⁶
If we are going to differentiate the equation in terms of x, we get the value for velocity.
dx/dt = 9.8t - 0.6t⁵
Calculate for the value of t when dx/dt = 0.
dx/dt = 0 = (9.8 - 0.6t⁴)(t)
The values of t from the equation is approximately equal to 0 and 2.
If we substitute these values to the equation for displacement,
(0) , x = 2.31 + 4.90(0²) - 0.1(0⁶) = 2.31
(2) , x = 2.31 + 4.90(2²) - 0.1(2⁶) = 15.51
Thus, the positions at the instants where velocity is zero are 2.31 and 15.51 meters.
