The position-time ( x-t ) graph for two cars, A and B, is shown in the given figure. Car A starts from a positive initial position and its graph makes an angle of 30^ with the time axis. Car B starts from the origin and its graph makes an angle of 30^ with the position axis. What is the ratio of the velocity of car A to the velocity of car B?

Step-by-step solution

The velocity of a particle is given by the slope of its position-time graph, i.e., v = , where is the angle made by the graph with the time axis. For car A, the angle with the time axis is _A = 30^ . Velocity of car A, v_A = 30^ = 1 3 For car B, the angle with the position axis is 30^ . Therefore, the angle with the time axis is _B = 90^ - 30^ = 60^ . Velocity of car B, v_B = 60^ = 3 The ratio of the velocity of car A to the velocity of car B is: v_A v_B = 1/ 3 3 = 1 3 Thus, the required ratio is 1 : 3 . Answer: 1