rate of change of velocity with respect to time.
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Vibration has amplitude and frequency, usually defined by acceleration and cycles per second (Hertz). It is measured with an accelerometer.
Units that are used for measures in which the direction is relevant. Example are displacement, velocity, acceleration, force.
With great difficulty. Acceleration is a vector and that means that it has a direction as well as a magnitude (size). For motion in a plane, the only effective way to show acceleration is to draw lots of arrows from points at regular intervals in a plane such that the length of the arrow is a measure of the magnitude of the acceleration and the direction of the arrow coincides with that of the acceleration. An answer referring to a speed-time graph is totally incorrect. That measures speed in the radial direction only. All apects of motion (displacement, speed, acceleration) in a transsverse direction are completely ignored.
Measures of motion (displacement, velocity, acceleration) and forces are all vectors so any study involving these would require vector calculus.
Gravitational acceleration is simply acceleration due to gravity.