How long does it take an automobile traveling in the left lane at 84 km/h to overtake another car that is traveling in the right lane at 33 km/h, when the cars' front bumpers are initially 84 m apart?
The car in the left lane is traveling at 84 km/h. Coverting the units of the speed to m/s this is equal to 23.33 m/s. Similarly the car in the right lane is traveling at 33 km/h. In terms of m/s this is equal to 9.167 m/s
The difference between the speed of the two cars is 14.163 m/s. In one second the car in the left lane moves 14.163 m closer to the car in the right lane. Initially the two cars are separated by a distance equal to 84 s.
For the car in the left lane to overtake the car in the right lane it has to move closer to the car in the right lane by 84 m. The time required for it to do so is equal to 84/14.163 = 5.93 s
The car in the left lane overtakes the car in the right lane in approximately 5.93 s.
Speed of car in the left lane = 84 Km/h = (84*1000)/(60*60) m/s
=> 23.33 m/s
Similarly the speed of the car in the right lane = 33 Km/s = 9.17 m/s
Relative speed of car in the left lane with respect to the car in the right lane = diference in speed of 2 cars = 23.33-9.17 = 14.16 m/s
Distance to be covered to overtake the car = 84 m
Time taken to cover the distance of 84 meters with a speed of 14.16 m/s = 84/14.16 = 5.93 s
Time required to overtake the car in right lane is 5.93 seconds