A car travels along a straight stretch of road. It proceeds for 14 mi at 50 mi/h, then 28.3 mi at 48 mi/h, and finally 37.4 mi at 38.3 mi/h.
What is the car’s average velocity during
the entire trip?
Answer in units of mi/h
avg velocity= totaldistance/totaltime
can u show me the steps to the problem.
thanks
To find the average velocity during the entire trip, we need to calculate the total displacement and divide it by the total time taken.
First, let's find the total displacement by summing up the individual displacements. The displacement for each segment of the trip is the distance traveled since it is a straight road.
Displacement for the first segment: 14 mi
Displacement for the second segment: 28.3 mi
Displacement for the third segment: 37.4 mi
Total displacement: 14 mi + 28.3 mi + 37.4 mi = 79.7 mi
Next, let's calculate the total time taken. We need to find the time for each segment and add them together.
Time for the first segment: 14 mi / 50 mi/h = 0.28 h
Time for the second segment: 28.3 mi / 48 mi/h ≈ 0.589 h (rounded to three decimal places)
Time for the third segment: 37.4 mi / 38.3 mi/h ≈ 0.976 h (rounded to three decimal places)
Total time taken: 0.28 h + 0.589 h + 0.976 h ≈ 1.845 h (rounded to three decimal places)
Finally, we can calculate the average velocity by dividing the total displacement by the total time taken.
Average velocity = Total displacement / Total time taken
Average velocity = 79.7 mi / 1.845 h
Average velocity ≈ 43.23 mi/h (rounded to two decimal places)
Therefore, the car's average velocity during the entire trip is approximately 43.23 mi/h.