Question

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Answer 1

The ratio of velocity of body A to the velocity of body B is 1:3

Explanation:

We know that velocity is rate of change of displacement

i.e. $v=\frac{dx}{dt}$

From calculus we know that $\frac{dx}{dt}$ is nothing but slope of displacement-time graph

Therefore, from figure, the slope of line OA will be the velocity of body A and slope of line OB will be velocity of body B

The tangent of the angle that the lone OA makes with the x-axis is its slope

Thus, slope of line OA

$=\tan 30^\circ$

$=\frac{1}{\sqrt{3}}$

Therefore, velocity of body A

$v_A=\frac{1}{\sqrt{3}}$

Similarly, slope of line OB

$=\tan 60^\circ$

$=\sqrt{3}$

Therefore, velocity of body B

$v_B=\sqrt{3}$

Thus,

$\frac{v_A}{v_B}=\frac{1/\sqrt{3}}{\sqrt{3}}$

$\implies \frac{v_A}{v_B}=\frac{1}{3}$

or, $v_A:v_B=1:3$

Hope this answer is helpful,

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Answer 2

RATIO OF VELOCITY OF BODY A TO THE VELOCITY OF BODY B

To find the ratio,

we should first know what velocity actually means.

Velocity - The rate of change of position with respect to time is known as velocity.

Velocity is dx/dt.

where dx/dt is change in position or displacement wrt time.

According to the graph, velocity of Body A will be calculated by taking the slope of OA whereas the velocity of Body B will be calculated by taking the slope of OB.

Slope can be calculated by taking the tangents of both OA and OB. Let us calculate the slope respectively :-

• Slope of OA = Tan 30°

Va = 1/√3

• Slope of OB = Tan 60°

Vb = √3

Ratio of the velocities is as under :-

Va / Vb = (1/√3) ÷ √3

= (1/√3) × (1/√3)

= 1/3

=> Va : Vb = 1 : 3