a car is moving at 100 km/hr is 0.5 km behind another car moving at 60 km/h how far does the first car travel before it catches the second car?
To find out how far the first car travels before catching up to the second car, we need to determine the time it takes for the first car to catch up.
First, let's convert the speeds to meters per second for consistent units. Since 1 km = 1000 meters and 1 hour = 3600 seconds, the first car's speed is 100 km/h * (1000 m/km) / (3600 s/h) = 27.78 m/s, and the second car's speed is 60 km/h * (1000 m/km) / (3600 s/h) = 16.67 m/s.
Next, let's determine the relative speed between the two cars. The first car is moving at 27.78 m/s, while the second car is moving at 16.67 m/s. Therefore, the relative speed between the two cars is 27.78 m/s - 16.67 m/s = 11.11 m/s.
Now, to find the time it takes for the first car to catch up, we divide the initial distance between them by the relative speed:
Time = Distance / Relative Speed.
The initial distance between the two cars is 0.5 km * (1000 m/km) = 500 meters. Plugging the values into the formula, we get:
Time = 500 m / 11.11 m/s = 45.01 seconds.
Finally, to find how far the first car travels, we multiply its speed by the time it takes:
Distance = Speed * Time.
Distance = 27.78 m/s * 45.01 seconds = 1250.06 meters.
Therefore, the first car travels 1250.06 meters before catching up to the second car.