Question

Give scientific reason for acceleration has time factor twice

Answer 1

from definition of acceleration, it is the rate of change of velocity. and we know, velocity is the rate of change of displacement.

so, acceleration is the double differentiable function of displacement.

didn't get it ?

okay, lets us consider a suitable example. let displacement is variable with time as x(t) = t² - 3t + 2

so, velocity will be , dx/dt = 2t - 3 [ because velocity is the rate of change of displacement ]

but acceleration will be , dv/dt = 2 [ because acceleration is the rate of change of velocity. ]

now mathematically, acceleration can be written as $a=\frac{dv}{dt}\:or,\:\frac{d^2x}{dt^2}$

now, see 2nd expression d²x/dt² , it is clearly shown acceleration has time factor twice.

okay, you can see by one more operation.

find unit of acceleration :

unit of acceleration = unit of velocity/unit of time or unit of displacement/unit of time ² = m/s²

hence, it is clear that acceleration has time factor twice.