The initial velocity of a particle is $u$ (at $t = 0$) and the acceleration ${n^{th}}$ is given by $at$. Which of the following relation is valid
$v = u + a{t^2}$
$v = u + a\frac{{{t^2}}}{2}$
$v = u + at$
$v = u$
Draw $x \to t$ graph for positive acceleration.
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