Question

The displacement-time graph of a particle moving along a straight line is shown in the figure.

The acceleration-time graph of this particle is

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Given, $x=9 t^{2}$
$\therefore v=\frac{d x}{d t}=\frac{d}{d t}\left(9 t^{2}\right)=\frac{9 d}{d t}\left(t^{2}\right)=18 t$
also, $a=\frac{d^{2} x}{d t^{2}}=\frac{d v}{d t}=\frac{d}{d t}(18 t)=18$
So, the graph between acceleration and time is a line parallel to time axis as acceleration is constant.