JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Kinematics

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}

5 m / s

then

v_{2} =

_______

m / s

Answer: 10

Solution

Average velocity is the total distance over the total time:

v_{a v g} = \frac{x + \frac{3 x}{2}}{\frac{x}{v _{1}} + \frac{3 x}{2 v _{2}}} = \frac{5/2}{\frac{1}{5} + \frac{3}{2 v _{2}}}

. Setting this equal to

\frac{50}{7}

gives

\frac{1}{5} + \frac{3}{2 v _{2}} = \frac{7}{20}

, hence

\frac{3}{2 v _{2}} = \frac{3}{20}

and

v_{2} = 10

m/s.

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Integer answer

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