Kinematics Questions

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times 10^{-2}\cos \pi t$ metres. The time at which the maximum speed first occurs is:

The velocity of a particle is $v=v_0+gt+f{t}^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time ($t=1$) is:

A point mass oscillates along the $x$ -axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then:

A particle is projected at $60^{\circ }$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is: