Velocity (m/s)-time (s) graph is plotted for the motion of two cars A and B for 10 s, when the cars are initially at rest and acquire final velocities as V_A and V_B, respectively. The respective straight lines of the graph make angles 30° and 60°, respectively with the x-axis (time). The difference in velocities V_B and V_A is

In a velocity-time (v-t) graph, the slope of the line represents the acceleration (a) of the object. For an object starting from rest (u = 0), the final velocity (v) after time t is given by the formula: v = at.

The slope of the graph is equal to the tangent of the angle (θ) it makes with the time-axis (x-axis). Therefore, acceleration a = tan θ.

• For car A: a_A = tan 30° = 1/√3. Thus, V_A = a_A × 10 = 10/√3 m/s.
• For car B: a_B = tan 60° = √3. Thus, V_B = a_B × 10 = 10√3 m/s.

The difference in velocities is:
V_B - V_A = 10√3 - 10/√3
V_B - V_A = 10(√3 - 1/√3) = 10((3 - 1)/√3) = 20/√3 m/s.

Note: Option A (20/13) is a typographical representation of 20/√3.