A car, starting from rest, accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is $15S$, then

What will be change in speed of moving object if both speed and acceleration are positive or negative ?

A particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a=4\,t$. If it starts from the origin, the distance covered by it in $3\,s$ is $...........\,m$

The position of a particle moving along the $X-$axis at certain times is given below :Which of the following describes the motion correctly

$\begin{array}{|c|c|c|c|c|} \hline t( s ) & 0 & 1 & 2 & 3 \\ \hline x ( m ) & -2 & 0 & 6 & 16 \\ \hline \end{array} $

A particle of mass $m$ moves on the x-axis as follows : it starts from rest at $t = 0$ from the point $x = 0$ and comes to rest at $ t= 1$ at the point $x = 1$. No other information is available about its motion at intermediate time $(0 < t < 1)$. If $\alpha $ denotes the instantaneous acceleration of the particle, then

A particle moves a distance $x$ in time $t$ according to equation $x = (t + 5)^{-1}$ The  acceleration of particle is proportional to