A car travels along a straight stretch of road.
It proceeds for 11.4 mi at 57 mi/h, then
21.8 mi at 43 mi/h, and finally 30.8 mi at
32.6 mi/h.
What is the car’s average velocity during
the entire trip?
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To find the car's average velocity during the entire trip, we need to calculate the total displacement and divide it by the total time taken.
First, let's calculate the total displacement. The car traveled 11.4 mi at 57 mi/h, which means it took (11.4 mi) / (57 mi/h) = 0.2 hours to cover that distance. The displacement during this part is 11.4 mi in the positive direction.
Next, the car traveled 21.8 mi at 43 mi/h, taking (21.8 mi) / (43 mi/h) = 0.51 hours. The displacement during this part is another 21.8 mi in the positive direction.
Finally, the car traveled 30.8 mi at 32.6 mi/h, taking (30.8 mi) / (32.6 mi/h) = 0.94 hours. The displacement during this part is another 30.8 mi in the positive direction.
Now, let's calculate the total time taken. The car took 0.2 hours + 0.51 hours + 0.94 hours = 1.65 hours for the entire trip.
To find the total displacement, we add the individual displacements: 11.4 mi + 21.8 mi + 30.8 mi = 63 mi.
Now let's calculate the average velocity. Average velocity is given by total displacement divided by total time: average velocity = total displacement / total time = 63 mi / 1.65 hours ≈ 38.1818 mi/h.
Therefore, the car's average velocity during the entire trip is approximately 38.1818 mi/h.