Question

A car is moving along a circular arc at a speed of 20 ms^-1 . The radius of the arc is 10 m. If the speed is increased at the rate of 30 ms^-2, what is the resultant acceleration ?

Moderate

Solution

Here, $a_{r} = \frac{v^{2}}{r} = \frac{20 \times 20}{10} = 40 {ms}^{- 2}$
$\begin{array}{l} a_{r} = 30 {ms}^{- 2} \\ a = \sqrt{a_{r}^{2} + a_{t}^{2}} = \sqrt{30^{2} + 40^{2}} \\ = 50 {ms}^{- 2} \end{array}$
Hence (2) is the choice

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