The displacement-time of two moving particles make angle of 30° and 45° with the X-axis. The ratio of their velocities is ______

CONCEPT:

• Velocity: The displacement per unit time is called velocity.

$v=\frac{\Delta x}{\Delta t}$

where v is the velocity, Δx is the change in displacement, Δt is the change in time.

• In the graph of displacement and time, The slope of the graph gives velocity (v).

$v=\frac{\Delta x}{\Delta t}=tan\theta$

where v is the velocity, Δx is the change in displacement, Δt is the change in time, and θ is the angle of line in the graph.

CALCULATION:

For the displacement - time graph:

$v=tan\theta$

$\frac{v_1}{v_2}=\frac{tan{\theta }_1}{tan{\theta }_2}=\frac{tan30}{tan45}=\frac{1/\sqrt{3}}{1}$

v₁ : v₂ = 1 : √3

So the correct answer is option 4.