During the first 18 minutes of a 1.0-hour trip, a car has an average speed of 11 m/s. What must the average speed of the car be during the last 42 minutes of the trip be if the car is to have an average speed of 21 m/s for the entire trip?
1hour = 3600s.
d = 21m/s * 3600s=75600m = t0tal distance to be traveled.
t1 = 18min.=18min * 60s/min = 1080s.
d1 = 11m/s * 1080s = 11880m. = Distanced traveled.
d2 = d - d1,
d2 = 75600 - 11880 = 63720m = distance remaining.
t2 = 42min = 42min * 60s/min = 2520s = Time remaining.
V(avg) = d2 / t2 = 63720 / 2520 = 25.3m/s = Average speed during t2.
CHECK:
V(avg) = d / (t1 + t2) = 75600 / 3600 = 21m/s = Average speed for the trip.
Nice explanation
Good
To find the average speed of the car during the last 42 minutes of the trip, we need to use the formula for average speed:
Average Speed = Total Distance / Total Time
First, let's find the total distance traveled during the first 18 minutes of the trip. Since the car's average speed during this time is given as 11 m/s, we can calculate the distance as:
Distance = Speed × Time
Distance = 11 m/s × 18 minutes
Distance = 198 meters
Next, let's find the total distance traveled during the entire trip. Since we have the average speed for the entire trip given as 21 m/s, we can calculate the distance using the formula:
Distance = Speed × Time
Distance = 21 m/s × 1.0 hour
Since 1.0 hour is equal to 60 minutes, we can substitute this value:
Distance = 21 m/s × 60 minutes
Distance = 1260 meters
Now, subtract the distance traveled during the first 18 minutes from the total distance to find the distance traveled during the last 42 minutes:
Distance traveled in the last 42 minutes = Total distance - Distance traveled in the first 18 minutes
Distance traveled in the last 42 minutes = 1260 meters - 198 meters
Distance traveled in the last 42 minutes = 1062 meters
Finally, we can calculate the average speed during the last 42 minutes by using the formula:
Average Speed = Total Distance / Total Time
Since the time is given as 42 minutes, we can substitute the values:
Average Speed = 1062 meters / 42 minutes
Average Speed = 25.29 m/s
Therefore, the average speed of the car during the last 42 minutes of the trip must be approximately 25.29 m/s to have an average speed of 21 m/s for the entire trip.