A car travels along a straight stretch of road.

It proceeds for 11.2 mi at 52 mi/h, then
23.2 mi at 40 mi/h, and finally 48.2 mi at
31.9 mi/h.
What is the car’s average velocity during
the entire trip?

figure out how long the whole trip took

t = 11.2/52 + 23.2/40 + 48.2/31.9

and

how many miles total?
d = 11.2 + 23.2 + 48.2

then

average speed = d/t

since the was no change in direction, the speed is the magnitude of the velocity with no directions specified.

( poor wording of question, velocity is a vector with magnitude and DIRECTION. Speed is just a scalar. For speed use a speedometer. For velocity you need the speedometer AND a compass)

To find the average velocity of the car during the entire trip, we need to calculate the total displacement and divide it by the total time taken.

First, we need to find the total displacement. Displacement is the change in position, which can be calculated by subtracting the initial position from the final position.

The initial position is 0 miles because the car starts at the beginning of the road. The final position is the sum of the distances traveled for each segment. Adding the distances gives us:

Total distance = 11.2 mi + 23.2 mi + 48.2 mi = 82.6 mi

Now, we need to find the total time taken for the entire trip. We divide the distance traveled in each segment by the corresponding speed to find the time taken for each segment:

Time taken for the first segment = 11.2 mi / 52 mi/h = 0.215 hours
Time taken for the second segment = 23.2 mi / 40 mi/h = 0.58 hours
Time taken for the third segment = 48.2 mi / 31.9 mi/h = 1.51 hours

Total time = 0.215 hours + 0.58 hours + 1.51 hours = 2.305 hours

Now, we can calculate the average velocity by dividing the total displacement by the total time:

Average velocity = Total displacement / Total time
Average velocity = 82.6 mi / 2.305 hours
Average velocity ≈ 35.85 mi/h

Therefore, the car's average velocity during the entire trip is approximately 35.85 mi/h.