The position $x$ of a particle varies with time $t$ as $x = at^2 - bt^3$. The acceleration of the particle will be zero at time $t$ equal to

What is retardation? What is its direction?

$A$ particle moves along the $x$-axis and its displacement $x$ varies with time $t$ according to the equation $x = c_0(t^2 - 2) + c(t - 2)^2$,where $c_0$ and $c$ are constants of appropriate dimensions. Which of the following statements is correct?

$A$ body in one-dimensional motion has zero speed at an instant. At that instant,it must have:

$A$ particle starts from rest. Its acceleration $a$ versus time $t$ is shown in the figure. The maximum speed of the particle will be (in $m/s$)

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