A car is travelling at $30 \mathrm{~ms}^{-1}$ speed on a circuiar road of radius $300 \mathrm{~m}$. If its…
A car is travelling at $30 \mathrm{~ms}^{-1}$ speed on a circuiar road of radius $300 \mathrm{~m}$. If its speed is increasing at the rate of 4 $\mathrm{ms}^{-2}$, then its acceleration is
$2.7 \mathrm{~ms}^{-2}$
$3 \mathrm{~ms}^{-2}$
$4 \mathrm{~ms}^{-2}$
$5 \mathrm{~ms}^{-2}$
Solution
Velocity of car, V=30 m/s Radius of road, $\mathrm{R}=300 \mathrm{~m}$.
Tangential acceleration, $a_T=4 \mathrm{~m} / \mathrm{s}^2$ Centripetal acceleration, $\mathrm{a}_{\mathrm{C}}=\frac{\mathrm{V}^2}{\dot{\mathrm{R}}}$
$
\therefore a_C=\frac{30 \times 30}{300}=3 \mathrm{~m} / \mathrm{s}^2
$
Net acceleration is given as:
$
\begin{aligned}
& \mathrm{a}_{\mathrm{T}}=\sqrt{\mathrm{a}_{\mathrm{T}}{ }^2+\mathrm{a}_{\mathrm{C}}{ }^2}=\sqrt{(3)^2+(4)^2} \\
& \mathrm{a}_{\mathrm{T}}=5 \mathrm{~m} / \mathrm{s}^2
\end{aligned}
$