The displacement-time graph of two moving particles make angles of...

The displacement-time graph of two moving particles make angles of

30^{\circ}

and

45^{\circ}

with the

X

-axis. The ratio of their velocities is
The displacement-time graph of two moving particles make angles of 30^ and 45^ with the X -axis. The ratio of their

The displacement-time graph of two moving particles make angles of 30^ and 45^ with the X -axis. The ratio of their

Options

A $\sqrt{3}: 2$
B $1: 1$
C $1: 2$
D $1: \sqrt{3}$

Correct answer

D. $1: \sqrt{3}$

Step-by-step solution

By the definition, the slope of displacement-time graph is velocity. i.e.,

\quad v=\tan \theta

\therefore \quad \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}}

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