At some instant, a motor car is moving on a circular path of radius 600 m, with a speed u = 30 m s−1

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At some instant, a motor car is moving on a circular path of radius 600 m, with a speed u = 30 m s−1. If its speed is increased at a rate of 2 m s−2, the magnitude of the acceleration of the car at that instant is :

Accepted Answer

[Key Concept: Tangential and centripetal accelerations are perpendicular, so they add as vectors.]

$$\begin{matrix} & a_{C} = a_{R} = \frac{v^{2}}{R} = \frac{(30)^{2}}{600} = \frac{900}{600} = \frac{3}{2}\text{~[Centripital acceleration]~} \\ & a_{t} = 2 \\ & a_{Net} = \sqrt{a_{t}^{2} + a_{c}^{2}} \\ & \ = \sqrt{(2)^{2} + (3/2)^{2}} = \sqrt{\frac{25}{4}} = \frac{5}{2} \\ & a_{net} = 2.5\text{ }m/s^{2} \end{matrix}$$

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