A train starting from rest travels the first part of its journey with constant acceleration $a$ , second part with constant velocity $v$ and third part with constant retardation $a$ , being brought to rest. The average speed for the whole journey is $\frac{{7v}}{8}$. The train travels with constant velocity for $...$ of the total time
$0.75$
$0.87$
$0.83$
$1.28$
A small block slides without friction down an inclined plane starting from rest. Let ${S_n}$be the distance travelled from time $t = n - 1$ to $t = n.$ Then $\frac{{{S_n}}}{{{S_{n + 1}}}}$ is
The correct statement from the following is
A dancer moves counterclockwise at constant speed around the path shown below. The path is such that the lengths of its segments, $PQ, QR, RS$, and $SP$, are equal. Arcs $QR$ and $SP$ are semicircles. Which of the following best represents the magnitude of the dancer’s acceleration as a function of time $t$ during one trip around the path, beginning at point $P$ ?
A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x -$ axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration, $v =$ velocity, $x =$ displacement, $t =$ time)
The velocity of a particle moving in the positive direction of $x$-axis varies as $v=5 \sqrt{x}$. Assuming that at $t=0$, particle was at $x=0$. What is the acceleration of the particle $.........m/s^2$