First slide

Work Energy Theorem

Question

A running man has half the kinetic energy that a body half his mass has. The man speeds up by f m/s and then has the same kinetic energy as the boy. The original speed of the man is

Easy

A

$(1 + \sqrt{2}) m / s$
B

$(2 + \sqrt{2}) m / s$
C

$(3+ \sqrt{2}) m / s$
D

$\sqrt{2} m / s$

Solution

$Given that E_{1} = E_{2} / 2 or \frac{1}{2} m v_{1}^{2} = \frac{1}{2} (\frac{1}{2} \times \frac{m}{2} \times v_{2}^{2}) or v_{2} = 2 v_{1} Finally, \frac{1}{2} m {(v_{1} + 1)}^{2} = \frac{1}{2} \times \frac{m}{2} \times v_{2}^{2} = \frac{1}{2} \times \frac{m}{2} \times {(2 v_{1})}^{2} V_{1} = (\sqrt{2} + 1) m / s$

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