Question

In the case of a body falling freely from small height:

• A. The change in position is equal in equal intervals of time.
• B. The change in velocity is equal in equal intervals of time.
• C. The change in acceleration is zero in equal intervals of time.
• D. All the above are true.

Answer 1

Answer: (B), (C)

The change in acceleration is zero in equal intervals of time.
The change in velocity is equal in equal intervals of time.

Consider time interval $T\in (t_1,t_2)\text{where}{t}_2-t_1=c\text{where c is a constant}$

Assume body is dropped from rest from a height h.

Displacement $s=ut+\frac{1}{2}a{t}^2$

$s=-\frac{1}{2}g{t}^2$
Position at time $t$ w.r.t ground $x=h-\frac{1}{2}g{t}^2$

Change in position in time interval $T,\Delta x=\frac{1}{2}g(t_1^2-t_2^2)\ne constant$

$v=u+at$
$v=-gt$

Change in velocity in time interval $T,\Delta v=g(t_1-t_2)=-gc=constant$

Now,
$g\to$const
$\therefore$ acceleration due to gravity is constant and the changes of acceleration is zero in equal intervals of time.