A particle's velocity is given by $v = 4 - 2t$, where $t$ is in seconds and $v$ is in m/s. If the particle starts at $x = 2$ m at $t = 0$, at what time does the particle instantaneously change its direction of motion?

If a car is moving with a constant velocity of 10 m/s towards the east, what is its acceleration?

Out of the following functions representing motion of a particle which represents SHM (i) $y = \sin \omega t - \cos \omega t$ (ii) $y = {\sin ^3}\omega t$ (iii) $y = 5\cos \left( {\frac{{3\pi }}{4} - 3\omega t} \right)$ (iv) $y = 1 + \omega t + {\omega ^2}{t^2}$

The displacement equation of a particle is $x = 3\,\,\sin \,\,2t + 4\,\,\cos \,\,2t.$ The amplitude and maximum velocity will be respectively

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

The equations for displacements of two particles working $SHM$ are represented by ${y_1} = A\sin (\omega t + \emptyset )$ and ${y_2} = A\cos \omega t$. The phase difference between the velocities of the two particles is

A particle executes $SHM$ with amplitude $0.5\,cm$ and frequency $100\,\,{s^{ - 1}}$. The maximum speed of the particle is $\left[ {in\,\,m/s} \right]$

A body undergoes SHM with an amplitude of $5$ cm. At a displacement of $3$ cm from the mean position, the magnitudes of its velocity and acceleration are equal. What is the time period of the SHM?

A car travels 30 m in 2 seconds and then 40 m in another 3 seconds in the same direction. What is its average speed?

The displacement of a particle executing SHM is given by $y = 0.25{\rm{ }}sin{\rm{ }}200t{\rm{ }}\,\,\,cm$ the maximum speed of the particle is

A body is vibrating in simple harmonic motion. If its acceleration is 12 ${\rm{cm}}{{\rm{s}}^{ - 2}}$ at a displacement 3 cm, then time period is