Question 114 of 308

The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$.
The acceleration-time $(a, t)$ graph for the motion of the body will be

ABCD

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Answer: (B)

Distance along a line i.e., displacement ( $s$ ) $=t^3\left(\because s \propto t^3\right.$ given $)$
By double differentiation of displacement, we get acceleration.
$V=\frac{d s}{d t}=\frac{d t^3}{d t}=3 t^2$ and
$$\begin{aligned} & a=\frac{d v}{d t}=\frac{d 3 t^2}{d t}=6 t \\ & a=6 t \text { or } a \propto t \end{aligned}$$
Hence graph (b) is correct.

JEE Main Physics practice question on Kinematics (Graphs of motion in one dimension), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.