Cars A and B, each moving at 70 km/h, are approaching one another on a straight highway. After how many seconds will they meet if they were initially 1 km apart?
The distance between the cars diminishes at a rate of 140 km/h. If the initial separation distance is 1 km, the time to meet is 1/140 hour, or 25.7 seconds
To find out the time it takes for Cars A and B to meet, we can use the formula:
Distance = Speed × Time
Both cars are moving towards each other, so their speeds should be added:
Total Speed = Speed of Car A + Speed of Car B = 70 km/h + 70 km/h = 140 km/h
The relative speed of the two cars is 140 km/h. Now we can calculate the time it takes for the cars to meet:
Time = Distance / Speed = 1 km / (140 km/h) = 0.0071 hours
To convert this time to seconds, we need to multiply by 60 minutes per hour (60 minutes/hour) and 60 seconds per minute (60 seconds/minute):
Time = 0.0071 hours × 60 minutes/hour × 60 seconds/minute ≈ 25.56 seconds
Therefore, Cars A and B will meet after approximately 25.56 seconds if they were initially 1 km apart.
To find the time it takes for Cars A and B to meet, we can make use of the formula for relative velocity:
Relative velocity = Speed of Car A + Speed of Car B
In this case, both cars are moving towards each other, so their relative velocity is the sum of their individual speeds.
Relative velocity = 70 km/h + 70 km/h = 140 km/h
Now, we need to convert the relative velocity to meters per second because the distance we have is in meters.
1 km = 1000 meters
1 hour = 60 minutes = 60 seconds
So, 140 km/h can be converted to meters per second as follows:
140 km/h = (140 km/h) * (1000 m/km) * (1 h/3600 s)
= (140 * 1000) / 3600 m/s
= 38.8889 m/s (rounded to four decimal places)
Now that we know the relative velocity is 38.8889 m/s, we can find the time it takes for Cars A and B to meet using the formula:
Time = Distance / Relative velocity
In this case, the initial distance between the cars is 1 km, which is equal to 1000 meters.
Time = 1000 m / 38.8889 m/s
= 25.71 seconds (rounded to two decimal places)
Therefore, it will take approximately 25.71 seconds for Cars A and B to meet if they were initially 1 km apart.