Question

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

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Distance along a line i.e., displacement (s)
$=t^3$ ($\because s\propto t^3$ given)
By double differentiation of displacement, we get acceleration.
$V=\frac{ds}{dt}=\frac{d{t}^3}{dt}=3t^2$ and
$a=\frac{dv}{dt}=\frac{d3t^2}{dt}=6t$
$a=6t$ or $a\propto t$
Hence graph $\left(b\right)$ is correct.