Question

A particle moves in a circle of radius $1cm$ at a speed given by $v=2t$, where $v$ is in $cm/s$ and $t$ is in seconds. Total acceleration of the particle at $t=1$ second is $2\sqrt{n}cm/s^2$ Find value of $n$.

Answer 1

Given $v=2t$. Then, tangential acceleration
$a_t=\frac{dv}{dt}=2cm/s^2$ (at $t=1s)$
and centripetal acceleration
$a_n=\frac{v^2}{R}=\frac{4t^2}{1}=4cm/s^2$
$\therefore a_{net}=\sqrt{a_t^2+a_n^2}=2\sqrt{5}cm/s^2$
$\therefore n=5$