Acceleration versus time graph of a body starting from rest is shown in the figure. The velocity versus time graph of the body is given by

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 car, moving with a speed of $50 \,km/hr$, can be stopped by brakes after at least $6\,m$. If the same car is moving at a speed of $100 \,km/hr$, the minimum stopping distance is..........$m$

A ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).

$(a)$ Plot qualitatively velocity versus time graph.

$(b)$ Plot qualitatively acceleration versus time graph.

A particle starts moving along a line from zero initial velocity and comes to rest after moving distance $d$. During its motion, it had a constant acceleration $f$ over $2 / 3$ of the distance and covered the rest of the distance with constant retardation. The time taken to cover the distance is

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4{t^2}$ and $y = 5t$, where $x$ and $y$ are in metre and $t$ in seconds. The acceleration of particle at $t = 5\;s$ is.........$m/{s^2}$