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.

\(v = {Δ x \over Δ t}\)

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).

\(v = {Δ x \over Δ t} = tan θ\)

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:

\(v = tan θ\)

\({v_1 \over v_2} = { tan θ_1 \over tan \theta_2} = { tan30 \over tan 45}={ 1/ \sqrt3 \over 1}\)

v₁ : v₂ = 1 : √3

So the correct answer is option 4.