From the position time graph for two particles and B is shown below- Graph A and particles A making angles - nbsp- 60- nbsp- and - nbsp- 30- nbsp- with the time axis- The ratio of velocities - nbsp- v-A - v-B nbsp- is- 1-3- 1-1- 4-1- -2- - 1-

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Position Time Graph

From the posi...

Question

From the position time graph for two particles and B is shown below. Graph A and particles A making angles $60^{\circ}$ and $30^{\circ}$ with the time axis. The ratio of velocities $v_{A} : v_{B}$ is

1 : 1

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4 : 1

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\sqrt{2} : 1

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1 : 3

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Solution

The correct option is A $1 : 3$
The slope of the distance - time graph gives the speed of the object.

For the particle $A$ , the slope of the line is $t a n θ_{1} = t a n 30 = \frac{1}{\sqrt{3}}$

For the particle $B$ , the slope of the line is $t a n θ_{2} = t a n 60 = \sqrt{3}$

Thus, ratio of the velocities, $\frac{v_{A}}{v_{B}} = \frac{t a n 30}{t a n 60} = \frac{1 / \sqrt{3}}{\sqrt{3}} = \frac{1}{3}$

So, the ratio is $1 : 3$

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