a woman drives at a speed of 20m/s for part of a trip and at a speed of 30m/s for the rest of the trip if she spends 10 minutes driving at each speed determine her average speed for the full trip. If instead she drives 10 kilometers at each speed determine her average speed for the full trip.
10 min = 600 s
600 s (20 m/s + 30 m/s) = 30 km
ave spd = 30 km / 20 min = 1.5 km/min
10 km / 20 m/s = 500 s
10 km / 30 m/s = 1000/3 s
20 km / (1500/3 s + 1000/3 s) =
... 60 / 2500 km/s = 36/25 km/min =
... 1.44 km/min
a. (20+30)/2 = 25 m/s. = Avg. speed.
b. 20*t1 = 10,000m., t1 = 500 s.
30*t2 = 10,000m, t2 = 333.3 s.
Total time = t1+t2 = 500 + 333.3 = 833.3 s.
Avg. speed = (d1+d2)/(t1+t2) = 20,000/833.3 = 24 m/s.
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To determine the average speed for the full trip, we need to consider the total distance traveled and the total time taken.
First, let's calculate the total distance for each part of the trip:
For the first part of the trip, traveling at 20 m/s for 10 minutes, the distance covered can be calculated using the formula: distance = speed × time.
Distance1 = 20 m/s × 10 minutes.
For the second part of the trip, traveling at 30 m/s for 10 minutes:
Distance2 = 30 m/s × 10 minutes.
Now, if the time and speed are given in the same unit, such as meters and seconds, we can directly calculate the average speed using the formula: average speed = total distance / total time.
Average Speed = (Distance1 + Distance2) / (time1 + time2).
Let's substitute the values and calculate the average speed:
Average Speed = (Distance1 + Distance2) / (10 minutes + 10 minutes).
If the values are not given in the same unit, like in the case where distance is given in kilometers and time is given in minutes, we need to convert the units so they are consistent.
If instead of using meters and seconds, we consider the distance in kilometers and time in minutes, we can first convert the minutes to hours by dividing by 60:
10 minutes = 10 minutes / 60 minutes/hour.
Now, let's calculate the distance:
Distance1 = 20 m/s × 10 minutes / 60 minutes/hour.
Distance2 = 30 m/s × 10 minutes / 60 minutes/hour.
And calculate the average speed:
Average Speed = (Distance1 + Distance2) / (10 minutes + 10 minutes) / 60 minutes/hour.
Let's substitute the values and calculate the average speed:
Average Speed = (Distance1 + Distance2) / (10 minutes + 10 minutes) / 60 minutes/hour.
In this case, if we want to consider 10 kilometers for each part of the trip, we need to convert the distance into meters. Since 1 kilometer is equal to 1000 meters, we can multiply the distance in kilometers by 1000 to get the distance in meters.
Now, let's calculate the average speed using the same formula:
Average Speed = (Distance1 + Distance2) / (10 kilometers + 10 kilometers).
Let's substitute the values and calculate the average speed:
Average Speed = (Distance1 + Distance2) / (10 kilometers + 10 kilometers).