Two particles P and Q are moving along the x-axis. Their position-time graphs are straight lines making angles of 60^ and 30^ respectively with the time axis. If the axes are drawn in SI units, the magnitude of the relative velocity of P with respect to Q is:

Step-by-step solution

The velocity of a particle is given by the slope of its position-time graph, which is the tangent of the angle it makes with the time axis. The velocity of particle P is: v_P = (60^ ) = 3 m/s The velocity of particle Q is: v_Q = (30^ ) = 1 3 m/s Since both slopes are positive, the particles are moving in the same direction along the x-axis. The magnitude of the relative velocity of P with respect to Q is: v_ PQ = |v_P - v_Q| = 3 - 1 3 v_ PQ = 3 - 1 3 = 2 3 m/s Answer: 2 3 m/s