You drive a car 1400 to the east, then 2400 to the north. The trip took 3.0 minutes.

What was the direction of your average velocity?

What was the magnitude of your average velocity?

For some reason I seem to be lacking ability to answer these questions. I tried displacement/time but I got it wrong what do you guys think?

Displacement take into account of the direction, and does not take into account of the intermediate steps. Distance is the linear measurement.

For example, if you go east 10 km, and then north 10 km, and then west 10 km. You finish at at point at 10 km north of the initial position.
The displacement is 10 km north.
The distance is 30 km.

The same applies to your problem.

The separate displacements are
1400 units east, 2400 units north.
If we take the cartesian plan with east=x-axis, and north=y-axis, the displacement is (1400,2400).
The magnitude of the displacement is
√(1400²2400²)
=2778.5 units
The direction is given by
tan-1(y/x)
=tan-1(2400/1400)
=59.74°

The magnitude of the displacement is

√(1400²+2400²)

The average velocity is the displacement divided by time, in this case, in units/min, or any other that you see fit.

To determine the direction of your average velocity, you need to consider the displacement in each direction separately. The displacement in the eastward direction is 1400 m, and the displacement in the northward direction is 2400 m. To calculate the direction of the average velocity, you need to find the tangent of the angle between the eastward direction and the northward direction.

In this case, the tangent of the angle can be found using the formula:

tan(θ) = (displacement north) / (displacement east)

tan(θ) = 2400 / 1400

Using a calculator, you can find the value of θ to be approximately 58.96 degrees (rounded to two decimal places).

Therefore, the direction of your average velocity is approximately 58.96 degrees north of east.

Now let's move on to finding the magnitude of your average velocity. The magnitude of velocity is calculated by dividing the total displacement by the total time taken.

Total displacement = √((displacement east)^2 + (displacement north)^2)

Total displacement = √((1400^2) + (2400^2))

Total displacement ≈ 2788.85 m

Total time taken = 3.0 minutes = 180 seconds

Average velocity = Total displacement / Total time taken

Average velocity ≈ 2788.85 m / 180 s ≈ 15.49 m/s

Therefore, the magnitude of your average velocity is approximately 15.49 m/s.

To summarize:

Direction of average velocity: Approximately 58.96 degrees north of east.
Magnitude of average velocity: Approximately 15.49 m/s.