## Understand that the acceleration vector is in the direction of the change of the velocity vector. In one dimensional (straight line) motion,

Question

Understand that the acceleration vector is in the direction of the change of the velocity vector. In one dimensional (straight line) motion, acceleration is accompanied by a change in speed, and the acceleration is always parallel (or antiparallel) to the velocity. When motion can occur in two dimensions (e.g. is confined to a tabletop but can lie anywhere in the x-y plane), the definition of acceleration is

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2 days 2021-07-22T14:43:05+00:00 1 Answers 1 views 0

a = √ (a_t² + a_c²)

a_t = dv / dt
,    a_c = v² / r

Explanation:

In a two-dimensional movement, the acceleration can have two components, one in each axis of the movement, so the acceleration can be written as the components of the acceleration in each axis.

a = aₓ i ^ + a_y j ^

Another very common way of expressing acceleration is by creating a reference system with a parallel axis and a perpendicular axis. The axis called parallel is in the radial direction and the perpendicular axis is perpendicular to the movement, therefore the acceleration remains

a = √ (a_t² + a_c²)

where the tangential acceleration is

a_t = dv / dt

the centripetal acceleration is

a_c = v² / r