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Question 1 of 5

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The formula for finding the kinetic energy, [tex][tex]$E$[/tex][/tex], of an object is given below, where [tex][tex]$m$[/tex][/tex] represents the mass of the object.

[tex]E = \frac{1}{2} m v^2[/tex]

Solve the formula for [tex]v[/tex].

A. [tex]v = \sqrt{\frac{2 E}{m}}[/tex]

B. [tex]v = \frac{4 E^2}{m}[/tex]

C. [tex]v = \sqrt{\frac{E}{2 m}}[/tex]

D. [tex]v = \sqrt{\frac{m}{2 E}}[/tex]

Sagot :

GinnyAnswer
To solve the given kinetic energy formula for velocity [tex]\( v \)[/tex], let's go through the steps methodically:

The formula for kinetic energy is:
[tex]\[ E = \frac{1}{2} m v^2 \][/tex]

We need to solve this equation for [tex]\( v \)[/tex].

1. Multiply both sides by 2 to isolate the term involving [tex]\( v \)[/tex]:
[tex]\[ 2E = m v^2 \][/tex]

2. Divide both sides by [tex]\( m \)[/tex] to solve for [tex]\( v^2 \)[/tex]:
[tex]\[ v^2 = \frac{2E}{m} \][/tex]

3. Take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]

So, the correct formula for [tex]\( v \)[/tex] is:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]

Therefore, the correct answer is:
[tex]\[ v = \sqrt{\frac{2E}{m}} \][/tex]
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