A car travels along a straight stretch of road if receipts for 13.6 miles at 55 mph than 25.8 miles at 48 mph and finally 43.1 miles at 33 mph what is the cart average velocity during the entire trip answer in units of miles per hour
avg speed = (total distance)/(total time)
since time = distance/speed, we have an average speed of
(13.6+25.8+43.1)/(13.6/55 + 25.8/48 + 43.1/33) = 39.46 mi/hr
To find the average velocity of the car during the entire trip, you need to calculate the total displacement and divide it by the total time taken.
First, let's calculate the total displacement of the car. The displacement is the change in position or distance traveled by the car.
For the first segment, the car travels 13.6 miles at a speed of 55 mph. So the displacement for this segment is 13.6 miles.
For the second segment, the car travels 25.8 miles at a speed of 48 mph. Again, the displacement for this segment is 25.8 miles.
For the third segment, the car travels 43.1 miles at a speed of 33 mph. Therefore, the displacement for this segment is 43.1 miles.
To find the total displacement, you add up the displacements of the three segments:
Total displacement = 13.6 miles + 25.8 miles + 43.1 miles = 82.5 miles
Next, let's calculate the total time taken by the car. To do this, we need to find the time taken for each segment and sum them up.
For the first segment, the distance is 13.6 miles, and the speed is 55 mph. Using the formula time = distance / speed, you can calculate the time taken for this segment:
Time taken for the first segment = 13.6 miles / 55 mph = 0.2473 hours
Similarly, for the second segment, the distance is 25.8 miles, and the speed is 48 mph. So the time taken for the second segment is:
Time taken for the second segment = 25.8 miles / 48 mph ≈ 0.5375 hours
Finally, for the third segment, the distance is 43.1 miles, and the speed is 33 mph. Thus, the time taken for the third segment is:
Time taken for the third segment = 43.1 miles / 33 mph ≈ 1.3061 hours
To find the total time for the entire trip, add up the times for the three segments:
Total time = 0.2473 hours + 0.5375 hours + 1.3061 hours ≈ 2.0909 hours.
Now, we can find the average velocity by dividing the total displacement by the total time:
Average velocity = Total displacement / Total time = 82.5 miles / 2.0909 hours ≈ 39.4 mph.
Therefore, the average velocity of the car during the entire trip is approximately 39.4 miles per hour.