Is the magnitude and direction of gravity on an object the same as the objects vertical velocity? I need to make a diagram for an entry level college physics class.  I need to show the magnitude and direction of gravity on a flying object and also show the magnitude and direction of the objects vertical velocity.  This seems redundant, aren't these the same basic measurement?
Magnitude and direction of gravity:  downwards at a rate of $9.8\, m/s^2$
Magnitude and direction of vertical velocity:  downwards at a rate of $9.8\, m/s^2$ (right?)
I thought these would be the same, but for some reason that seems wrong to have to diagram both of these parameters if they are in fact the same magnitude and direction.
Am I correct, magnitude and direction of both gravity and vertical velocity are the same?  Or are they different?
Thanks for the help!
 A: Gravity acceleration is... acceleration, measured in $\mathrm{m/s^2}$. It is the rate of change of the velocity..
Velocity is measured in $\rm m/s$. It is the rate of change of the position.
The vertical velocity and the acceleration due to gravity of a body are collinear but they can have different magnitudes as well different orientations. Think about a ball thrown upwards. Think of its velocity during the upward movement, the instant when it stops and when it falls. Compare it with the acceleration due to gravity.
A: No.  Acceleration and velocity have different units, so their magnitudes cannot be compared.  Whether one is larger than the other numerically depends on what units are used.
Acceleration and velocity can have the same direction, but this is not necessary - eg a ball thrown upwards has upward velocity but downward acceleration, until it reaches maximum height and falls back to Earth, when they are both downwards.
Perhaps what you need to do is show a diagram of forces not acceleration/velocity.
An airplane which is flying horizontally at constant speed has no vertical velocity, only horizontal velocity.  Because it is moving at constant velocity (no acceleration - ie no change in speed or direction) Newton's 1st Law tells us the resultant force on it is zero.  Vertically the downward force of gravity (weight) is balanced by the upward aerodynamic lift on the wings.  Horizontally the forward thrust from the engines is balanced by the backward drag resistance of the air.
