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

A body starts from the origin and moves along the $X-$axis such that the velocity at any instant is given by $(4{t^3} - 2t)$, where $t$ is in sec and velocity in$m/s$. What is the acceleration of the particle, when it is $2\, m$ from the origin..........$m/{s^2}$

A particle moves in a straight line and its position $x$ at time $t$ is given by $x^2=2+t$. Its acceleration is given by

$Assertion$ : Retardation is directly opposite to the velocity.
$Reason$ : Retardation is equal to the time rate of decrease of speed.

An object with a mass $10 \,kg$ moves at a constant velocity of $10 \,m/sec$. A constant force then acts for $4\, second$ on the object and gives it a speed of $2\, m/sec$ in opposite direction. The acceleration produced in it, is ........ $m/{\sec ^2}$