Question

what does negative velocity even mean

Answer 1

Negative velocity means that the body or the mover moves with the velocity magnitude (say 15 m/s) but in the opposite direction you are familiar with.

Answer 2

so hes just moving left

Answer 3

GREAT!

Answer 4

@3mar

Could you check this very basic work?

Answer 5

Velocity can be in terms of vectors, so negative just means direction.

Answer 6

You can think of moving in one direction as a cumulative function of displacement. The more you move in one direction, the further you get from where you started, but if you turn around and move in the opposite direction, you bring the "net" distance traveled to zero. So when your velocity \(v\) is positive, you move some positive distance \(x\) away from your starting point. When you turn around and move at the same velocity, but now opposite direction, you're essentially subtracting from \(x\) until it goes back to zero: \(v+(-v)=0\). (If you're familiar with calculus, this is kind of the idea behind why the integral of the velocity function represents the displacement function.)

What you're doing doesn't give the magnitude of displacement. You're not even subtracting displacements here because the graphs give you *velocity*, so your work actually has you subtracting the final and initial velocities.

In the first graph you have a constant negative velocity, so you're moving at a constant speed away from the start. You do not turn around, which means you must be making some non-zero change to your displacement and thus the displacement in scenario A is not computed correctly. To get the right answer, you should be using
\[\text{velocity}=\frac{\text{displacement}}{\text{time}}\implies\text{displacement}=\text{velocity}\times\text{time}\]which translates to finding the unsigned area between the velocity functions and the time axis.