The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The…
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
Solution
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
