The displacement $x$ of a particle along a straight line at time $t$ is given by $x = {a_0} + {a_1}t + {a_2}{t^2}$. The acceleration of the particle is

Position $x$ of a particle at any instant is related with velocity as $v = \sqrt {2x + 9}$ . The particle starts from origin. Then initial acceleration and velocity are

The velocity $(v)$ of a particle moving along $x$-axis varies with its position $x$ as shown in figure. The acceleration $(a)$ of particle varies with position $(x)$ as

A particle of unit mass undergoes one­ dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ - 2n}}$, 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

A particle moves along $x$-axis in such a way that its $x$-co-ordinate varies with time according to the equation $x=4-2 t+t^2$. The speed of the particle will vary with time as

A body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are