Question

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as $x=2cos(0.5\pi t+\frac{\pi }{3})$
The magnitude of the maximum acceleration of the particle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$x=2cos(0.5\pi t+\frac{\pi }{3})\therefore VelocityV=\frac{dx}{dt}=-2\times 0.5\pi sin(0.5\pi t+\frac{\pi }{3})\therefore Accelerationa=\frac{dv}{dt}=-2\times 0.5\pi \times 0.5\pi cos(0.5\pi t+\frac{\pi }{3})\therefore Maximumacceleration,a_{max}=-2\times 0.5\pi \times 0.5\pi =-\frac{{\pi }^2}{2}cm{s}^{-2}\therefore orMagnitudeis\left|a_{max}\right|=|-\frac{{\pi }^2}{2}|=\frac{{\pi }^2}{2}cm{s}^{-2}$
Hence the correct choice is (c)