Question

A car travels north at \(30.0 \mathrm{~m} / \mathrm{s}\) for \(10.0 \mathrm{~min}\). It then travels south at \(40.0 \mathrm{~m} / \mathrm{s}\) for \(20.0 \mathrm{~min}\). What are the total distance the car travels and its displacement?

Short answer

Answer: The total distance traveled is 66,000 meters, and the displacement is 30,000 meters southwards.

Step-by-step solution

Convert time to seconds

To maintain consistent units, convert the given time (in minutes) to seconds by multiplying the time by 60. For the north trip: \(10.0 \mathrm{min} \times 60 \mathrm{s/min} = 600\mathrm{s}\) For the south trip: \(20.0 \mathrm{min} \times 60 \mathrm{s/min} = 1200\mathrm{s}\)

Calculate the distance traveled in each direction

To do this, multiply the speed by the time for each direction (north and south): For the north trip: distance = speed \(\times\) time \(= 30.0\mathrm{m/s} \times 600\mathrm{s} = 18000\mathrm{m}\) For the south trip: distance = speed \(\times\) time \(= 40.0\mathrm{m/s} \times 1200\mathrm{s} = 48000\mathrm{m}\)

Calculate the total distance traveled

Add up the distances covered in both directions (north and south). Total distance = distance north + distance south \(= 18000\mathrm{m} + 48000\mathrm{m}= 66000\mathrm{m}\)

Calculate the displacement

Since the car traveled in opposite directions (north and south), we need to find the difference between the two distances: Displacement = distance south - distance north \(= 48000\mathrm{m} - 18000\mathrm{m} = 30000 \mathrm{m}\) (southwards) Now, we have the total distance traveled and the displacement: Total distance = \(66000\mathrm{m}\) Displacement = \(30000\mathrm{m}\) (southwards)