Answer:
e) 11 m/s
Explanation:
For a particle under the action of a conservative force, its mechanical energy at point 0 is must be equal to its mechanical energy at point 1:
![K_1+U_1=K_0+U_0\\\\\frac{mv_1^2}{2}+[(8.0\frac{J}{m^2})(x_1)^2+(2.0\frac{J}{m^4})(x_1)^4]=\frac{mv_0^2}{2}+[(8.0\frac{J}{m^2})(x_0)^2+(2.0\frac{J}{m^4})(x_0)^4]](https://tex.z-dn.net/?f=K_1%2BU_1%3DK_0%2BU_0%5C%5C%5C%5C%5Cfrac%7Bmv_1%5E2%7D%7B2%7D%2B%5B%288.0%5Cfrac%7BJ%7D%7Bm%5E2%7D%29%28x_1%29%5E2%2B%282.0%5Cfrac%7BJ%7D%7Bm%5E4%7D%29%28x_1%29%5E4%5D%3D%5Cfrac%7Bmv_0%5E2%7D%7B2%7D%2B%5B%288.0%5Cfrac%7BJ%7D%7Bm%5E2%7D%29%28x_0%29%5E2%2B%282.0%5Cfrac%7BJ%7D%7Bm%5E4%7D%29%28x_0%29%5E4%5D)
In 
the speed is given, so 
and 
. Replacing:
![\frac{mv_1^2}{2}+[(8.0\frac{J}{m^2})(1m)^2+(2.0\frac{J}{m^4})(1m)^4]=\frac{mv_0^2}{2}+[(8.0\frac{J}{m^2})0^2+(2.0\frac{J}{m^4})(0)^4]\\\frac{mv_1^2}{2}+8.0J+2.0J=\frac{mv_0^2}{2}\\\frac{mv_0^2}{2}=\frac{mv_1^2}{2}+10J\\v_0=\sqrt{\frac{2}{m}(\frac{mv_1^2}{2}+10J)}\\v_0=\sqrt{\frac{2}{0.2kg}(\frac{(0.2kg)(5\frac{m}{s})^2}{2}+10J)}\\v_0=11.18\frac{m}{s}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv_1%5E2%7D%7B2%7D%2B%5B%288.0%5Cfrac%7BJ%7D%7Bm%5E2%7D%29%281m%29%5E2%2B%282.0%5Cfrac%7BJ%7D%7Bm%5E4%7D%29%281m%29%5E4%5D%3D%5Cfrac%7Bmv_0%5E2%7D%7B2%7D%2B%5B%288.0%5Cfrac%7BJ%7D%7Bm%5E2%7D%290%5E2%2B%282.0%5Cfrac%7BJ%7D%7Bm%5E4%7D%29%280%29%5E4%5D%5C%5C%5Cfrac%7Bmv_1%5E2%7D%7B2%7D%2B8.0J%2B2.0J%3D%5Cfrac%7Bmv_0%5E2%7D%7B2%7D%5C%5C%5Cfrac%7Bmv_0%5E2%7D%7B2%7D%3D%5Cfrac%7Bmv_1%5E2%7D%7B2%7D%2B10J%5C%5Cv_0%3D%5Csqrt%7B%5Cfrac%7B2%7D%7Bm%7D%28%5Cfrac%7Bmv_1%5E2%7D%7B2%7D%2B10J%29%7D%5C%5Cv_0%3D%5Csqrt%7B%5Cfrac%7B2%7D%7B0.2kg%7D%28%5Cfrac%7B%280.2kg%29%285%5Cfrac%7Bm%7D%7Bs%7D%29%5E2%7D%7B2%7D%2B10J%29%7D%5C%5Cv_0%3D11.18%5Cfrac%7Bm%7D%7Bs%7D)
Improved muscle strength and tone – to protect your joints from injury.
maintaining flexibility and balance, which can help you remain independent as you age.
weight management and increased muscle-to-fat ratio – as you gain muscle, your body burns more kilojoules when at rest.
Answer: Within any frame of reference that is accelerating
Special relativity was proposed on 1905 by Einstein, who developed his theory based on the following two postulates:
1. <em>The laws of physics are the same in all inertial systems. There is no preferential system.
</em>
2. <em>The speed of light in vacuum has the same value for all inertial systems.
</em>
Focusing on the first postulate, it can be affirmed that <u>any measurement on a body is made with reference to the system in which it is being measured</u>.
Now, taking into account that an inertial reference system is the one that complies with the principle of inertia:
<em>"For a body to have acceleration, an external force must act on it."</em>
The correct answer is
Within any frame of reference that is accelerating
Total mechanical energy = kinetic energy + potential energy
E = KE + PE
E = ½mv² + mgh
E = ½(0.1 kg)(2 m/s)² + (0.1 kg)(9.8 m/s²)(1.5 m)
E = 0.2 J + 1.47 J
E = 1.67 J
