Question

The following is the distance-time table of an object in motion

Time	0	1	2	3	4	5	6	7
Distance	0	1	8	27	64	125	216	343

In this case, the acceleration of the body

• A. cannot say
• B. Remains constant
• C. Increases with time
• D. Decreases with time

Answer 1

Answer: (C)

A careful observation of the distance-time table shows that $s\propto t^3$.
It is known that, in uniform motion $s\propto t$, and for motion with uniform acceleration $s\propto t^2$.
In the present case, $s\propto t^3$. Therefore, we conclude in this case that acceleration must be increasing with time.