Travelling at 60 km/h , a car overtakes another car travelling at 42 km/h . Assuming each car is 5.0 m long, determine the time taken during the overtake and the total road distance used for the overtake.

Step-by-step solution

The speeds of the two cars in m/s are: v_A = 60 5 18 = 50 3 m/s v_B = 42 5 18 = 35 3 m/s The relative speed of car A with respect to car B is: v_ rel = v_A - v_B = 50 3 - 35 3 = 5 m/s For car A to completely overtake car B, the front of car A must travel from the rear of car B to a point where the rear of car A is just ahead of the front of car B. The total relative distance to be covered is the sum of the lengths of both cars: d_ rel = L_A + L_B = 5.0 + 5.0 = 10.0 m The time taken for the overtake is: t = d_ rel v