First slide

The two types of acceleration

Question

In the given figure, $15 m s^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is

Moderate

A

$4.5 m s^{- 1}$
B

$5 m s^{- 1}$
C

$5.7 m s^{- 1}$
D

$6.2 m s^{- 1}$

Solution

$Here, a = 15 m s^{- 2}$
R = 2.5m
From fig,
$a_{c} = a \cos 30 ° = 15 \times \frac{\sqrt{3}}{2} m s^{- 2}$
$As we know, a_{c} = \frac{v^{2}}{R} \Rightarrow v = \sqrt{a_{c} R}$
$∴ v = \sqrt{15 \times \frac{\sqrt{3}}{2} \times 2.5} = 5.69 ≃ 5.7 m s^{- 1}$

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