A car is moving with a speed of $30 \mathrm{~ms}^{-1}$ on a circular path of radius $500 \mathrm{~m}$. If its speed is increasing at the rate of $2 \mathrm{~ms}^{-2}$, then find its acceleration.

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Aicharya · Accepted Answer

Given, initial speed, $u=30 \mathrm{~ms}^{-1}$ Radius, $r=500 \mathrm{~m}$ Linear acceleration, $a_T=2 \mathrm{~ms}^{-2}$ Let acceleration be $a$ $ \because \quad a=\sqrt{a_T^2+a_r^2} $ As, $a_r=\frac{u^2}{r}=\frac{(30)^2}{500}$ $ =\frac{900}{500}=\frac{9}{5} \mathrm{~ms}^{-2} $ $ \begin{aligned} 	herefore \quad a & =\sqrt{2^2+\left(\frac{9}{5}ight)^2}=\sqrt{4+\frac{81}{25}} \ & =2.69 \mathrm{~ms}^{-2} \simeq 2.7 \mathrm{~ms}^{-2} \end{aligned} $

A car is moving with a speed of $30 \mathrm{~ms}^{-1}$ on a circular path of radius $500 \mathrm{~m}$. If…

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