in a car, you drive from your home 4 km to the gas station, 8 km to the shopping mall to let your mother off, and 8.9 km back home. The trip takes 20 min. What is your velocity?

So I got 17.4 m/s but my teacher told me that the velocity is actually 0 m/s, can someone explain to me why?

Because you started and ended at the same place. There was no displacement.

Well, it seems like your teacher might be playing a little joke on you. Let's break it down. Velocity is the rate of change of displacement over time. If you have traveled a total distance of 20.9 km and it took you 20 minutes, we can calculate your average velocity.

Velocity = Total Displacement / Total Time

In this case, your total displacement is 0 km because you ended up back where you started. So, if we divide 0 km by 20 minutes (converted to hours), we get:

Velocity = 0 km / (20/60) hours = 0 km/h

So, technically, your teacher is correct. Your velocity is 0 km/h because you ended up back at home! However, keep in mind that this is just average velocity and doesn't account for the different distances covered during the trip.

To find the velocity, we need to divide the total distance traveled by the total time taken.

In this case, the total distance traveled is:
4 km (home to gas station) + 8 km (gas station to shopping mall) + 8.9 km (shopping mall back home) = 20.9 km

The total time taken for the trip is given as 20 minutes.

Now, let's convert the total distance to meters, as velocity is typically measured in meters per second (m/s):
20.9 km = 20,900 m

Similarly, let's convert the total time to seconds:
20 min = 20 × 60 = 1,200 s

Now we can calculate the velocity:
Velocity = Total distance ÷ Total time
Velocity = 20,900 m ÷ 1,200 s
Velocity ≈ 17.4 m/s

Based on these calculations, it appears that your initial calculation of 17.4 m/s is correct.

If your teacher said the velocity is 0 m/s, there might be some misunderstanding or miscommunication. It's possible that the velocity is being confused with speed, which is the magnitude of velocity without considering its direction. However, velocity is a vector quantity that includes both magnitude and direction. So, if the car started and ended at the same location (home), the displacement (change in position) would be zero, but the velocity can still be non-zero if the car had different velocities during different parts of the trip.

To determine your velocity, we need to first understand the definition of velocity. Velocity is a vector quantity that represents the rate at which an object changes its position. It is calculated by dividing the displacement of an object by the time taken to travel that distance.

In this case, the displacement can be determined by finding the total distance traveled and considering the direction. However, the fact that you return back to your home means that your displacement is zero. This is because displacement is a vector quantity, and in this scenario, the starting and ending points are the same.

To calculate velocity, we divide the displacement by the time taken. Since the displacement is zero, this means that velocity is also zero regardless of the time taken. Therefore, your teacher is correct in stating that the velocity is 0 m/s.