A car travels along a straight stretch of road. It proceeds for 15 mi at 51 mi/h, then 28.2 mi at 44 mi/h, and finally 36.4 mi at 39.3 mi/h.
What is the car’s average velocity during
the entire trip?
Answer in units of mi/h
D = 15 + 28.2 + 36.4 = 79.6mi = Total distanced traveled.
T = 15mi/51mi/h + 28.2mi/44mi/h + 36.4mi/39.3mi/h = 1.86h.
Vavg. = d / t = 79.6 / 1.86 = 42.8mi/h.
To find the car's average velocity during the entire trip, we need to calculate the total displacement and the total time taken.
First, let's find the total displacement of the car. The car travels 15 mi at 51 mi/h, 28.2 mi at 44 mi/h, and 36.4 mi at 39.3 mi/h. We can calculate the total displacement by summing up the individual displacements:
Displacement1 = Distance1 = 15 mi
Displacement2 = Distance2 = 28.2 mi
Displacement3 = Distance3 = 36.4 mi
Total displacement = Displacement1 + Displacement2 + Displacement3 = 15 mi + 28.2 mi + 36.4 mi = 79.6 mi
Now, let's find the total time taken by the car. The car travels at three different speeds for different distances, so we need to calculate the time for each segment:
Time1 = Distance1 / Speed1 = 15 mi / 51 mi/h
Time2 = Distance2 / Speed2 = 28.2 mi / 44 mi/h
Time3 = Distance3 / Speed3 = 36.4 mi / 39.3 mi/h
Total time taken = Time1 + Time2 + Time3
Now, we can find the average velocity by dividing the total displacement by the total time taken:
Average velocity = Total displacement / Total time taken
Let's plug in the values:
Average velocity = 79.6 mi / (Time1 + Time2 + Time3)
To calculate the average velocity, we need the values of Time1, Time2, and Time3, which can be obtained by simplifying the expressions above.
Once we have the values of Time1, Time2, and Time3, we can calculate the average velocity using the formula above.