**Problem Analysis:**
To find the average speed of the car, we need to calculate the total distance traveled by the car and the total time taken. Given the speeds of the car for different time intervals, we can calculate the distances traveled during each interval and then add them up to get the total distance. Similarly, we can calculate the total time taken by summing up the individual time intervals.

**Solution:**
Let's calculate the distance traveled during each interval and the total time taken.

1. Distance traveled in the first second:
Speed = 30 km/h
Time = 1 second
Distance = Speed * Time = 30 km/h * 1/3600 h = 30/3600 km = 1/120 km

2. Distance traveled in the next two seconds:
Speed = 40 km/h
Time = 2 seconds
Distance = Speed * Time = 40 km/h * 2/3600 h = 80/3600 km = 2/90 km

3. Distance traveled in the next three seconds:
Speed = 50 km/h
Time = 3 seconds
Distance = Speed * Time = 50 km/h * 3/3600 h = 150/3600 km = 5/120 km

Now, let's calculate the total distance and the total time taken:

Total Distance = Distance in the first second + Distance in the next two seconds + Distance in the next three seconds
= 1/120 km + 2/90 km + 5/120 km
= (1 + 8 + 5)/120 km
= 14/120 km
= 7/60 km

Total Time = Time in the first second + Time in the next two seconds + Time in the next three seconds
= 1 second + 2 seconds + 3 seconds
= 6 seconds

Finally, let's calculate the average speed:

Average Speed = Total Distance / Total Time
= (7/60 km) / 6 seconds
= (7/60 km) * (1/6) seconds
= 7/360 km/second

Therefore, the average speed of the car is 7/360 km/second.