The displacement-time graph for two particles A and B are straight lines

The displacement-time graph for two particles A and B are straight lines inclined at angles of

3 0^{o}

and

6 0^{o}

with the time axis. The ratio of their velocities is

1 : 3

. Let

v_{A}

and

v_{B}

be the velocity of particles A and B respectively. So

v_{A} : v_{B} = {Slope}_{A} : {Slope}_{B}

Also,

{Slope}_{A} : {Slope}_{B} = \tan 30 ° : \tan 60

{= > v}_{A} : v_{B} = \tan 30 ° : \tan 60 °

{= > v}_{A} : v_{B} = \frac{1}{\sqrt{3}} : \sqrt{3}

{= > v}_{A} : v_{B} = 1 : 3

The displacement-time graph for two particles A and B are straight lines inclined at angles of $3 0^{o}$ and $6 0^{o}$ with the time axis. The ratio of their velocities is