Indeed. It's been 10 years. Under ordinary circumstances, I imagine that should be long enough to start to grasp the concept of a reference frame - especially when it has been carefully explained.

So let's clear up Ghost's confusion.

We have a moving conveyer belt and a wheeled vehicle rolling along on the belt.

Consider the view of a person standing on the ground next to the conveyer belt. Call the direction to that person's right the positive x direction, and the direction to the left the negative x direction. Say that the belt is moving with speed v_belt to the left, from that person's point of view. Then its

*velocity* is -v_belt (with a minus sign to show that it's moving to the left). The person standing next to the belt sees the vehicle moving with a velocity of v_vehicle. Notice, I have not specified whether it is moving left or right, so v_vehicle could be positive or negative.

Next, consider the view of a person whose feet are glued to the conveyer belt. From that person's point of view, the speed of the belt is zero: it does not move relative to the person that is glued to it. Let the velocity of the vehicle, relative to this observer, be u, which could be positive or negative, depending on whether the vehicle is moving to the left or right according the person who is glued to the belt. The plus sign tells us that it moving to the right, according to the person who is glued to the conveyer belt.

The three velocities defined above are related by the following equation:

v_vehicle = +u - v_belt.

Let us now consider a few specific cases of these general equation.

__Case 1: u=0__

This is the case where the vehicle's speed relative to the observer on the belt is zero. That is, the vehicle remains at all times at a constant distance from the person who is glued to the belt. According to that person, the vehicle is stationary, hence u=0. Our equation above immediately gives us:

v_vehicle = 0 - v_belt = -v_belt.

This result tells us that the person on the ground, standing next to the belt, will see the vehicle moving to the left with the same speed as the belt, which makes perfect sense.

__Case 2: u=+v_belt__

This is the case where the glued observer sees the vehicle moving to the right along the belt, with a speed that happens to be equal to the belt's speed as measured by the person standing next to the belt. Our general equation gives:

v_vehicle = +v_belt - v_belt = 0

That is, the person on the ground sees that the vehicle is stationary relative to the ground. The distance between the observer standing next to the belt and the vehicle remains constant at all times. That observer sees the belt moving to the left and the vehicle's wheels trying to roll it along the belt to the right. The net effect is that the belt's leftward motion cancels out the vehicle's attempts to move towards the right, and the result is that the vehicle does not move at all relative to the ground observer.

__Case 3: u>+v_belt__

Our equation tells us that in this case v_vehicle > 0, which means the vehicle is moving to the right relative to the ground. This is the case where the vehicle is being "driven" rightwards along the belt faster than the belt is moving leftwards, from the point of view of the ground observer.

__Case 4: 0<u<+v_belt__

Our equation tells us that v_vehicle < 0, which means the vehicles moves leftwards relative to the ground. This is the case where the vehicle is "trying" to drive towards the right, but the belt is moving so fast to the left (relative to the ground) that the vehicle nevertheless ends up moving to the left (relative to the ground).

__Case 5: u<0__

Our equation tells us that v_vehicle < -v_belt. This is the case where the person who is stuck to the belt sees the vehicle driving leftwards along the belt. The person on the ground next to the belt sees the vehicle moving to the left at a greater speed, because not only is it "trying" to drive leftwards along the belt, but the belt is also carrying it along to the left.

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I think that covers all of the possibilities for the case of the belt moving to the left.