The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to \(v(x)= βx^{- 2 n}\) where \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\) is given by:

The acceleration of a particle starting from rest varies with time according to the relation \(A= - a\omega^2\sin \omega t\). The displacement of this particle at a time \(t\) will be:

A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right)\). At \(t=0\) particle is at the origin. From the following, select the correct position \((x)\) - time \((t)\) plot for the particle:

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