Solve the following :


A particle moves in a circle of radius $1.0 \mathrm{~cm}$ at a speed given by $\mathrm{v}=2.0 \mathrm{t}$ where $\mathrm{v}$ is in $\mathrm{cm} / \mathrm{s}$ and $\mathrm{t}$ in seconds. (a) Find the radial acceleration of the particle at $t=1 \mathrm{~s}$. (b) Find the tangential acceleration at $t=1 \mathrm{~s}$. (c) Find the magnitude of the acceleration at $t=1 \mathrm{~s}$.



Velocity of particle at $t=1 \mathrm{sec}$

$V=2 t$


$\mathrm{V}=2 \mathrm{~cm} / \mathrm{s}$

Radial acceleration


$A_{r}=4 c m / s^{2}$


Tangential acceleration

$\mathrm{A}_{t}=\frac{d v}{d t}=\frac{d(2 t)}{d t}$

$\mathrm{A}_{\mathrm{t}}=2 \mathrm{~cm} / \mathrm{s}^{2}$




$A_{n}=\sqrt{20} \mathrm{~cm} / \mathrm{s}$


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