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

The velocity- displacement graph of a particle is shown in figure.

$(a)$ Write the relation between $v$ and $x$.

$(b)$ Obtain the relation between acceleration and displacement and plot it.

A particle experiences a constant acceleration for $20\, seconds$ after starting from rest. If it travels a distance $s_1$ in the first $10\, seconds$ and distance $s_2$ in the next $10\, seconds$, then :-

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

If velocity of particle moving along $x-$ axis is given as $v = k\sqrt x $ . Then ($a$ is acceleration)

A Body moves $6\, m$ north. $8 \,m$ east and $10\;m$ vertically upwards, what is its resultant displacement from initial position