Question

A body moving along a straight line is covering distances which are directly proportional to the square of the time. What is the acceleration of the body if $K$ is the constant of proportionality?

• A. $2K$
• B. $3K$
• C. $\frac{K}{2}$
• D. $K^2$

Answer 1

The correct option is A $2K$

$Distance\left(s\right)\propto time(t{)}^2$

$\therefore s=K\times t^2$

$\therefore \frac{ds}{dt}=K\times \frac{d{t}^2}{dt}$

$\therefore velocity=\frac{ds}{dt}=K\times 2t$

$\frac{d^{2}s}{d{t}^2}=2K\times \frac{dt}{dt}$

$\therefore acceleation=\frac{d^{2}s}{d{t}^2}=2K$