A person travelling on a straight line moes with a uniform velocity for a distance x and with a uniform velocity for the next distance. The average velocity in this motion is m/s. If is 5 m/s then = __________ m/s. [2025]

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Solution

Q.
A person travelling on a straight line moves with a uniform velocity $v_{1}$ for a distance x and with a uniform velocity $v_{2}$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7}$ m/s. If $v_{1}$ is 5 m/s then $v_{2}$ = __________ m/s. [2025]

Ans.
(10)

$v_{avg} = \frac{x_{1} + x_{2}}{t_{1} + t_{2}}$

$\Rightarrow \frac{50}{7} = \frac{x + \frac{3 x}{2}}{\frac{x}{5} + \frac{3 x}{2 v_{2}}}$

$\Rightarrow \frac{50}{7} = \frac{5 / 2}{\frac{1}{5} + \frac{3}{2 v_{2}}}$

$\Rightarrow v_{2} = 10 m / s$

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