A particle moves along the x-axis such that its velocity $v$ varies with time $t$ as $v = At^2 + Bt + C$, where A, B, and C are constants. If the particle starts from rest at $t=0$ and its acceleration at $t=1$ second is $4 m/s^2$, and its velocity at $t=2$ seconds is $8 m/s$, what is the distance traveled by the particle in the first 2 seconds?

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 particle is projected vertically upwards with an initial speed 'u'. At a height 'h' above the ground, its speed is 'v'. What is the maximum height reached by the particle?

A particle performing SHM has time period $\frac{{2\pi }}{{\sqrt 3 }}$ and path length 4 cm. The displacement from mean position at which acceleration is equal to velocity is

A body describes $SHM$ with an amplitude of $50\,cm$ and a time period of 1.57 seconds. The velocity of the body when its displacement becomes $30\,cm$ is

A particle executing SHM has a maximum speed of $31.4$ cm/s and a maximum acceleration of $5$ m/s$^2$. Find the amplitude of oscillation.

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?

The motion which is not simple harmonic is

A simple harmonic wave having an amplitude A and time period T is represented by the equation $y = 5{\rm{sin \pi }}\left( {t + 4} \right){\rm{m}}.$ Then the value of A in (metre) and T in (second) are

The average velocity of a particle undergoing simple harmonic motion (SHM) over one complete oscillation is:

A particle moves so that its position vector is given by $\mathop {\rm{r}}\limits^ o \, = \,\cos {\rm{\omega }}\,{\rm{t}}\,{\rm{\hat x}}\,{\rm{ + }}\,{\rm{sin}}\,{\rm{\omega }}\,{\rm{t}}\,{\rm{\hat y}}{\rm{.}}$ Where ${\rm{\omega }}$ is a constant. Which of the following is true?