The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?
$v^2-u^2=2 k x$
$v^2=u^2+2 k x^2$
$v^2=u^2+k x^2$
$v^2+u^2=2 k x$
When acceleration and average acceleration are equal for moving object ?
Draw the $x\to t$ graphs for positive, negative and zero acceleration.
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 $...........\,m$
If velocity of particle moving along $x-$ axis is given as $v = k\sqrt x $ . Then ($a$ is acceleration)
A three-wheeler starts from rest, accelerates uniformly with $1\; m/s^{2}$ on a straight road for $10\; s$, and then moves with uniform velocity. Plot the distance covered by the vehicle during the $n ^{\text {th }}$ second $( n =1,2,3 \ldots .)$ versus $n$. What do you expect this plot to be during accelerated motion : a straight line or a parabola?