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- Thread starter Tabe
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futb0l

Velocity and Acceleration is a vector. That means it is a quantity WITH a direction. For example, I can assign the up direction as + and the down direction as -. Then when I drop an apple it will the acceleration = -g (negative), because it is going down. It is NOT possible to have a negative speed, but it is possible to have a negative VELOCITY.

Speed and Displacement is a vector - it is the quantity without direction.

Still don't understand? Try http://www.physicsclassroom.com/Class/1DKin/U1L1b.html

- #3

cepheid

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Velocity, on the other hand,

[tex] v_x [/tex] = 10 m/s if it is travelling in the positive x-direction

[tex] v_x [/tex] = -10 m/s if it is travelling in the negative x-direction

Since the object is travelling in a straight line, it obviously does not have components in any other direction (other than x!). So we can forget about the x and describe the object's velocity as v, a scalar that has an absolute value equal to the magnitude of the velocity vector, but unlike the magnitude, also has a sign that indicates the directional "sense" (+ or -) of the object's motion along the x-axis. We can write the velocity as

[tex] v [/tex] = 10 m/s if it is travelling in the positive x-direction

[tex] v [/tex] = -10 m/s if it is travelling in the negative x-direction

If you like, you can use the full blown vector notation instead:

[tex] \vec{v} = \text{(10 m/s)}\hat{i} [/tex]

(travelling in postive x-direction)

OR

[tex] \vec{v} = -\text{(10 m/s)}\hat{i} [/tex]

(travelling in negative x-direction).

One point of confusion to watch for (that only arises when the motion is confined along one axis and we choose to drop the x subscript). When using the scalar component notation, v indicates both magnitude (10m/s) and direction, which means it can be either postive or negative. In contrast, when using the vector notation, the same symbol "v" is actually the magnitude of the velocity vector:

[tex] v = |\vec{v}| [/tex]

so it is always positive (magnitudes are always postive). The direction is instead given by the sign on the unit vector:

[tex] \pm \hat{i} [/tex].

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