Question

The speed of a particle moving in a circle of radius $0.1m$ is $v = 1.0t$ where $t$ is time in second. The resultant acceleration of the particle at $t = 5s$ will be

• A. $10\mspace{6mu} m/s^{2}$
• B. $100\mspace{6mu} m/s^{2}$
• C. $250\mspace{6mu} m/s^{2}$
• D. $500\mspace{6mu} m/s^{2}$

Answer 1

Answer: (C)

$250\mspace{6mu} m/s^{2}$

Answer 2

$v = 1.0t$ $\Rightarrow$ $a_{t} = \frac{dv}{dt} = 1m/s^{2}$

and $a_{c} = \frac{v^{2}}{r} = \frac{(5)^{2}}{0.1} = 250m/s^{2}$ [At $t = 5{sec,}{}v = 5m/s$]

∴ $a_{N} = \sqrt{a_{c}^{2} + a_{t}^{2}} = \sqrt{(250)^{2} + 1^{2}}$ $\Rightarrow$ $a_{N} = 250m/s^{2}$ (approx.)