Question

Give scientific reasons for 1) acceleration has time factor twice 2)displacement is independent of its path

Answer 1

1. acceleration is the rate of change of velocity and also velocity is rate of change of displacement.

in mathematical, acceleration is second differentiation of displacement.e.g., $a=\frac{dv}{dt}=\frac{d^2s}{dt^2}$

dimensionally, velocity = [LT^-1]

time = [T]

so, acceleration = [LT^-1]/[T] = [LT^-2]

by this expression, it is clear that acceleration has time factor twice.

2. displacement is the minimum separation between starting point to finishing point.

or, displacement is the shortest distance between initial position to final position, hence it doesn't depend on path of particle.

so, displacement is independent of its path.