The velocity of a particle is given by $v = 2t^2 - 8t + 15 \,ms^{-1}$. Find its instantaneous acceleration at $t = 5 \,s$. (in $\,ms^{-2}$)

$A$ 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 ........ $m$.

The graph of position $x$ versus time $t$ represents the motion of a particle. The curve is a parabola opening upwards. If the equation of motion is given by $x = a + bt - ct^2$ where $b$ and $c$ are positive constants,which of the following expressions best describes the acceleration $a_{acc}$ of the particle?

What is retardation?

$A$ point moves in a straight line so that its displacement $x \ m$ at time $t \ s$ is given by $x^2 = 1 + t^2$. Its acceleration in $m/s^2$ at a time $t \ s$ is

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