Question

A motor car is travelling at 60 m/s on a circular road of radius 1200 m. It is increasing its speed at the rate of 4 $m / s^{2}$ . The acceleration of the car is:

Moderate

Solution

Tangential acceleration, $a_{t} = rα = 4 m / s^{2}$
Radial acceleration
$a_{t} = ω^{2} r = \frac{v^{2}}{r} = \frac{60 \times 60}{1200} = 3$ $m / s^{2}$
Hence, resultant acceleration of the car
a = $\sqrt{{a_{t}}^{2} + {a_{r}}^{2}} = \sqrt{4^{2} + 3^{2}} = 5 m / s^{2}$

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