A ball is thrown vertically upwards. Which of the following graphs correctly represents the variation of acceleration with time during its upward motion (neglecting air resistance)?

A particle's position vector is described by $\vec r = 2\cos \omega t\hat x + 2\sin \omega t\hat y$, where $\omega$ is constant. What is the path of the particle?

A particle moves along the x-axis with a velocity given by $v = 4t - 2$. What is its acceleration at $t = 2$ seconds?

Average velocity of a particle executing SHM in one complete vibration is:

A particle in SHM is described by the displacement function $x\left( t \right) = A\cos \left( {\omega t + {\rm{heta }}} \right)$ If the initial $\left( {t{\rm{ }} = {\rm{ }}0} \right)$ position of the particle is $1{\rm{ }}\,\,cm$ and its initial velocity is $\pi\,\, cm{s^{ - 1}}$ what is its amplitude? The angular frequency of the particle is $\pi\,\, {s^{ - 1}}$

A body moving with a constant velocity has:

A coin is placed on a horizontal platform, which undergoes horizontal SHM about a mean position O. the coin placed on platform does not slip, coefficient of friction between the coin and the platform is $\mu$. The amplitude of oscillation is gradually increased. The coin will begin to slip on the platform for the first time

This time period of a particle undergoing SHM is 16 s. It starts motion from the mean position. After 2 s, its velocity is $0.4{\rm{m}}{{\rm{s}}^{ - 1}}$ The amplitude is

A particle is executing S.H.M. Then the graph of acceleration as a function of displacement is

A particle moves in a straight line with a velocity given by $v = \alpha t + \beta t^3$, where $\alpha$ and $\beta$ are constants. If its acceleration at $t=1$ second is twice its acceleration at $t=0$, what is the relation between $\alpha$ and $\beta$?

A body executing simple harmonic motion has a maximum acceleration equal to $24\,\,m{s^{ - 2}}$ and maximum velocity of $16\,\,m{s^{ - 1}}$ ,the amplitude of the simple harmonic motion is