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Q.
A car is moving in a circular path of radius $500 \,m$ with a speed of $30 \,m/s$. If the speed is increasing, at the rate of $ 2\,m/s^2 $ the resultant acceleration will be
AMUAMU 2003
Solution:
A body moving in circular motion, has radial $\left(a_{R}\right)$ and tangential acceleration $\left(a_{T}\right)$. Hence, resultant acceleration is given by
$a=\sqrt{a_{T}^{2}+a_{R}^{2}}$
Given, $a_{T}=2 m / s ^{2}$,
$ a_{R} =\frac{v^{2}}{r}=\frac{30 \times 30}{500}=1.8 \,m / s ^{2} $
$ \therefore a=\sqrt{(1.8)^{2}+(2)^{2}}=\sqrt{7.24}$
$\Rightarrow a=2.69 \approx 2.7 \,m / s ^{2}$
