How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 20.0 km/h when the cars' front bumpers are initially 75 m apart?
The 75 m gap between cars is reduced at a rate of 60-20 = 40 km/h, which is 11.11 m/s.
Divide 75 by 11.11 for the number of seconds needed to close the gap.
To find out how long it takes for the automobile in the left lane to overtake the car in the right lane, you need to determine the relative speed between the two cars. Once you know the relative speed, you can calculate the time it will take for the left lane car to close the initial distance of 75 m.
The relative speed between the two cars can be found by subtracting the speed of the car in the right lane (20.0 km/h) from the speed of the car in the left lane (60.0 km/h).
Relative speed = Speed of left lane car - Speed of right lane car
Relative speed = 60.0 km/h - 20.0 km/h
Relative speed = 40.0 km/h
Now, you need to convert the relative speed from kilometers per hour to meters per second because the initial distance is given in meters. To convert km/h to m/s, you can multiply by (1000 m/3600 s).
Relative speed = 40.0 km/h * (1000 m/3600 s)
Relative speed = 11.1111 m/s (rounded to four decimal places)
Now that you have the relative speed, you can use this value to calculate the time it takes to close the initial distance of 75 m. Time can be calculated by dividing the distance by the relative speed.
Time = Distance / Relative speed
Time = 75 m / 11.1111 m/s
Time = 6.75 seconds (rounded to two decimal places)
Therefore, it will take approximately 6.75 seconds for the automobile in the left lane to overtake the car in the right lane when their front bumpers are initially 75 m apart.