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Question

$straight K space equals space fraction numerator 200 straight v squared over denominator 2 end fraction$
In the equation above, the kinetic energy, K , of a 200-gram object is given in terms of its speed, v. If the equation is rewritten in the form $straight v space equals space straight a space square root of straight K$ , where a is a positive constant, what is the value of a ?

0.1

The correct answer is: 0.1

HINT :- Rearrange the given equation and compare it with new equation.
Given , $straight K space equals space fraction numerator 200 straight v squared over denominator 2 end fraction space not stretchy rightwards double arrow space straight K space equals space 100 straight v squared space not stretchy rightwards double arrow space straight K space equals space left parenthesis 10 straight v right parenthesis squared space not stretchy rightwards double arrow space square root of straight K space equals space 10 straight v$
Substitute the value of $square root of straight K space end root in space straight v space equals space straight a space square root of straight K$
We get , $straight v space equals space straight a left parenthesis 10 straight v right parenthesis space not stretchy rightwards double arrow space 10 straight a space equals space 1$
a = $1 over 10$

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