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.
$V = \frac{ds}{dt} = \frac{dt^{3}}{dt} = 3t^{2}$ and
$a = \frac{dv}{dt} = \frac{d3t^{2}}{dt} = 6t$
$a = 6t$ or $a\, \propto\,t$
Hence graph $\left(b\right)$ is correct.