State true or false: if the positive x-axis points to the right and the x-component of velocity is negative, the cart must be moving to the left.

True

Explanation:

Velocity is a vector, therefore it consists of two elements:

- A magnitude (also called speed), which is the ratio between the displacement of the object and the time taken

- A direction, which corresponds to the direction of motion of the object

Therefore, velocity can be describes as positive or negative, depending on the direction which has been chosen as positive. If we chose the positive x-axis as positive direction, therefore:

- if the object is moving to the right (positive x-direction), the velocity will be positive

- if the object is moving to the left (negative x-direction), the velocity will be negative

So, in this case, since the velocity of the cart is negative, it must be moving to the left.

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it