A particle's position is given by $\vec r = A\cos \left( {\omega t + \phi } \right)\hat x + A\sin \left( {\omega t + \phi } \right)\hat y$, where $A$, $\omega$, and $\phi$ are constants. What type of motion does the particle exhibit?

A particle executes simple harmonic motion between $x$ $= - A\,\,{\rm{and}}\,\,x = + A$ The time taken for it to go from $0{\rm{ }}to\;A/2\,\,is\,\,{T_1}$ and to go from $A/2$ to $A\,\,{\rm{is}}\,\,{T_2}$ Then

A car traveling at 20 m/s decelerates at a constant rate of 2 m/s². How far will it travel before coming to rest?

A body moving with a constant velocity has:

An object's position in the x-y plane is described by $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$, where R is in meters and t is in seconds. What is the object's speed?

The amplitude of a particle performing SHM is ‘a’. The displacement at which its velocity will be a half the maximum velocity is

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

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?

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

A particle of 0.25 kg vibrates with a period of 2 second. If its greatest displacement is 0.4 m the maximum velocity in $m{s^{ - 1}}$ is

In SHM, the amplitude is $6$ cm. At what displacement from the mean position will the magnitude of velocity be equal to half the maximum velocity, if at a certain displacement, the magnitudes of velocity and acceleration are equal?