[1] In mechanics, acceleration is an object's velocity's change rate with time's respect. It's of ,any kinematics components and are vector quantities (have magnitude and direction). An object's acceleration's orientation is given by the net force's orientation acting on the object. An object's acceleration's magnitude, as depicted by Newton's 2nd law, is the combined effect of 2 causes:
Acceleration is fundamentally defined as velocity's 1st derivative with respect to time a = dv/dt
[B1] Acceleration can be both measured at a point in time (instantaneous acceleration) or over some finite time interval (average acceleration).
point in time: specific moment in duration
Constant acceleration is an object's velocity changes by the same amount at all time interval, drawn as a linear graph whether it's increasing/decreasing, which exists if both acceleration measures are the same for some time period, where average acceleration ā equals instantaneous acceleration a and both hold at 1 value no matter the time interval length chosen for Δt:
ā = a = Δt/Δt (if accceleration is constant)
[B1] Usual scenery moves have 3 key periods that acceleration is considered constant (Fig. 2.1):
during acceleration from 0 up to top speed (speed rises steadly ∴ acceleration is constant positive)
during travel at constant top speed (no velocity change ∴ acceleration is 0)
during deceleration to a stop (speed lowers steadly ∴ acceleration is constant negative)
Having acceleration as always constant is useful as it keeps the math of motion solely in algebra IO calculus, like in non-calculus physics courses.
Instantaneous acceleration is the velocity change rate at a specific time, found by taking the derivative of the velocity function or tangent line's slope on a velocity-time graph, representing how fast an object's speed/direction changes currently. It's the limit of average acceleration as the time interval shrinks to zero, expressed as a(t) = dv(t)/dt.
E.g., A ball falls from a height of 78.4 m, with 9.8 m/s2 gravity without resistance. To find the time it takes to hit the ground and the velocity prior impact.
Method 1 using algebra Via one of the 4 constant acceleration equation Δx = v1Δt + (aΔt2)/2 or fully written as Δx = x0 + v1Δt + (aΔt2)/2 (we often set the initial position x0 = 0)
[1] Wikipedia