Two cars, X and Y, are in uniform motion. The ratio of the speed of car X to the speed of car Y is 1:3 . If the position-time graph of car X makes an angle of 30^ with the time axis, what is the angle made by the position-time graph of car Y with the time axis?

Step-by-step solution

The slope of a position-time graph represents the velocity (or speed, for uniform motion in one direction) of the object. Let v_X and v_Y be the speeds of cars X and Y respectively. We know that v = ( ) , where is the angle made with the time axis. For car X: v_X = (30^ ) = 1 3 Given the ratio of speeds: v_X v_Y = 1 3 Substituting v_X : 1/ 3 v_Y = 1 3 v_Y = 3 3 = 3 For car Y: v_Y = ( _Y) = 3 _Y = 60^ The angle made by the position-time graph of car Y with the time axis is 60^ . Answer: 60^