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Q. The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time $X$ -axis The ratio of their velocities isPhysics Question Image

KCETKCET 2011Motion in a Straight Line

Solution:

By the definition, the slope of displacement-time graph is velocity.
i.e., $v=\tan \theta$
$\therefore \frac{v_{1}}{v_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$\frac{v_{1}}{v_{2}}=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}$
$\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{3}}$