The average acceleration of an object is defined to
be the change in velocity over a time interval divided by the duration
of the time interval. This principle applies when the object is moving
along any path; it need not be straight, and there is no requirement that
the acceleration be constant during the time period.
The principle is a relationship between 3 vectors (acceleration, initial
velocity and final velocity) and a scalar (duration). However, because
Andes accepts only scalar equations, you will be using the principle in
component form:
-
a_x = (vf_x - vi_x) / t, where a_x, vi_x and vf_x are the components along
the x-axis of the vectors*
-
a_y = (vf_y - vi_y) / t, where a_y, vi_y and vf_y are the components along
the y-axis of the vectors
Tip: Remember that acceleration is the VECTOR CHANGE in velocity divided
by the time duration, so the equation contains the VECTOR DIFFERENCE, that
is, the final velocity minus the initial velocity, not the sum.
This principle is potentially useful when the sought quantity is:
-
the duration of the time interval from Ti to Tf,
-
the average acceleration of the object over the time interval or one of
its components,
-
the velocity of the object at Ti, or
-
the velocity of the object at Tf.
* Note that in the special case where acceleration is constant, in magnitude
and direction, the equation for the final velocity at the end of a time
interval, t, is given by
-
vf_x = vi_x + a_x*t and
-
vf_y = vi_y + a_y*t
which are the same as the equations above with the terms rearranged.