The motion of a particle along a straight line is described by the function $x = (2t - 3)^2$,where $x$ is in metres and $t$ is in seconds. The acceleration of the particle at $t = 2 \,s$ is (in $\,m/s^2$)

What is retardation? What is its direction?

Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

The displacement of a particle,moving in a straight line,is given by $s = 2t^2 + 2t + 4$,where $s$ is in metres and $t$ is in seconds. The acceleration of the particle is ........ $m/s^2$.

$A$ particle moves along a straight line such that its displacement at any time $t$ is given by $s = (t^3 - 3t^2 + 2) \, m$. The displacement when the acceleration becomes zero is ........ $m$.

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 ........ $m/s^2$.