Question

The displacement of a particle is proportional to the cube of time elapsed. How does the acceleration of the particle depends on the obtained

• A. $\alpha \propto t^2$
• B. $\alpha \propto 2t$
• C. $\alpha \propto t^3$
• D. $\alpha \propto t$

Answer 1

The correct option is D $\alpha \propto t$

The displacement of a particle is proportional to the cube of time elapsed.

$x\propto t^3$

$x=k{t}^3$, where $k=$ proportionality constant

velocity, $v=\frac{dx}{dt}$

$v=3k{t}^2$

acceleration, $a=\frac{dv}{dt}$

$a=6kt$

$a\propto t$, acceleration of particle is directly proportional to elapsed time.

The corrrect option is D.