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E=(1)/(2)mv^2 Make v t he su bjec t of th is formula.

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E=(1)/(2)mv^2 Make v t he su bjec t of th is formula.

E=(1)/(2)mv^2 Make v t he su bjec t of th is formula.

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RosieMaster · Tutor for 5 years

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<p> v = \sqrt{\frac{2E}{m}}</p>

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<p> <br />Given is the formula of kinetic energy: \[E=\frac{1}{2} m v^{2}\]<br />We are required to solve it for \( v \).<br />First of all, it's useful to understand that the given equation is for finding the kinetic energy of a body in motion, in which:<br />- \( E \) corresponds to the energy (kinetic).<br />- \( m \) corresponds to the mass of the object<br />- \( v \) corresponds to the velocity<br />The equation as stated implies that the kinetic energy 'E' is a function of the mass of the object and its velocity. Since the question asked is to solve for velocity, we need to transform this equation so as to get 'v' on one side of the equation. <br />We have:<br />\[E=\frac{1}{2} m v^{2}\]<br />Multiplying both sides by 2, we have:<br />\[2E= m v^{2}\]<br />Now, to solve for \( v \), we divide both by \( m \) on both sides:<br />\[\frac{2E}{m}= v^{2}\]<br />Finally, to get 'v', we take square root on both side, which yields:<br />\[\sqrt{\frac{2E}{m}} = v\]<br />This gives us the required result. <br /></p>
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