Given below are two statements regarding the interpretation of position-time graphs for uniform motion: Statement I: If the position-time graphs of two moving particles make angles of 30^ and 60^ with the time axis, the ratio of their velocities is 1:2 . Statement II: The velocity of a particle in uniform motion is directly proportional to the angle its position-time graph makes with the time axis. In the light of th

Step-by-step solution

The velocity of a particle is given by the slope of its position-time graph, which is equal to the tangent of the angle ( ) the graph makes with the time axis, i.e., v = ( ) . Statement I is incorrect because the ratio of velocities for angles 30^ and 60^ is: v₁ v₂ = (30^ ) (60^ ) = 1/ 3 3 = 1 3 , not 1:2 . Statement II is incorrect because velocity is directly proportional to the tangent of the angle ( ( ) ), not the angle ( ) itself. For example, doubling the angle from 30^ to 60^ increases the velocity by a fact