A motorist drives south at 26.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.40 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.40 min trip, find the following values.

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To find the values, we need to use the equations of motion.

For the first part of the trip, when the motorist is driving south at 26.0 m/s for 3.00 min, we can calculate the distance covered using the equation:

distance = speed × time

distance = 26.0 m/s × (3.00 min × 60 s/min)

distance = 26.0 m/s × 180 s

distance = 4680 meters

For the second part of the trip, when the motorist turns west and travels at 25.0 m/s for 2.40 min, the distance covered can be calculated in the same way:

distance = 25.0 m/s × (2.40 min × 60 s/min)

distance = 25.0 m/s × 144 s

distance = 3600 meters

For the final part of the trip, when the motorist travels northwest at 30.0 m/s for 1.00 min, we can calculate the distance covered again:

distance = 30.0 m/s × (1.00 min × 60 s/min)

distance = 30.0 m/s × 60 s

distance = 1800 meters

To find the total distance covered, we add up the distances from each part of the trip:

total distance = 4680 meters + 3600 meters + 1800 meters

total distance = 10,080 meters

Now, let's find the displacement, which is the straight-line distance from the starting point to the ending point.

The displacement can be found using the Pythagorean theorem since the motorist traveled south and west, and then northwest:

displacement = √((total south-west distance)^2 + (total northwest distance)^2)

displacement = √((4680 meters + 3600 meters)^2 + 1800 meters^2)

displacement = √((8280 meters)^2 + 1800 meters^2)

displacement = √(68,438,400 meters^2 + 3,240,000 meters^2)

displacement = √(71,678,400 meters^2)

displacement = 8456.94 meters

Therefore, the total distance covered by the motorist is 10,080 meters, and the displacement is 8456.94 meters.