Question

If a particle moving along a line follows the law $t=a{s}^2+bs+c$, then the retardation of the particle is proportional to

• A. square of the velocity
• B. cube of the displacement
• C. cube of the velocity
• D. square of the displacement

Answer 1

The correct option is C cube of the velocity

$t=a{s}^2+bs+c$

$1=2as\frac{ds}{dt}+b\frac{ds}{dt}$

$v=\frac{ds}{dt}=\frac{1}{(2as+b)}$

$\Rightarrow \frac{dv}{dt}=-\frac{2a}{(2as+b{)}^3}$

$\Rightarrow \frac{dv}{dt}=-2a{v}^3$

Hence, retardation is proportional to cube of velocity.