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Question
A particle moves in a circle of radius 1.0 cm at a speed given by v = 2.0 t where v is cm/s and t in seconds.
(a) Find the radial acceleration of the particle at t = 1 s.
(b) Find the tangential acceleration at t = 1 s.
(c) Find the magnitude of the acceleration at t = 1 s.
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Solution
Speed is given as a function of time. Therefore, we have:
v = 2t
Radius of the circle = r = 1 cm
At time t = 2 s, we get :
(a) Radial acceleration
\[\text{a} = \frac{\text{v}^2}{\text{r}} = \frac{2 {}^2}{1} = 4 \text{ cm/ s}^2\]
(b) Tangential acceleration
\[\text{a} = \frac{\text{dv}}{\text{dt}}\]
\[ = \frac{d}{\text{{dt}}}\left( 2t \right) = 2 \text{ cm/ s}^2\]
(c) Magnitude of acceleration
\[a = \sqrt{4^2 + 2^2}\]
\[ = \sqrt{20} \text{ cm/ s}^2\]
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