For a body moving with uniform acceleration along a straight line, the variation of its velocity $(v)$ with position $(x)$ is best represented by:

$A$ particle is moving in a straight line with initial velocity $u$ and uniform acceleration $a$. If the sum of the distance travelled in the $t^{\text{th}}$ and $(t+1)^{\text{th}}$ seconds is $100 \text{ cm}$,then its velocity after $t$ seconds,in $\text{cm/s}$,is:

$A$ particle moves according to the equation $y = a + bt + ct^2 - dt^4$. What are the initial velocity and initial acceleration of the particle?

$A$ particle located at $x= 0$ at time $t= 0$ starts moving along the positive $x-$direction with a velocity $v$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle varies with time as:

$A$ body starts from rest. What is the ratio of the distance travelled by the body during the $4^{th}$ and $3^{rd}$ second?

$A$ car moving at a speed of $50 \, km/hr$ stops after covering a distance of $6 \, m$ upon applying brakes. If the same car is moving at a speed of $100 \, km/hr$,what distance (in $m$) will it cover after applying the brakes?