The stopping distance of a vehicle moving with a given acceleration is proportional to the ....... of its speed.

$A$ body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the coordinates ..........

The displacement of a particle after time $t$ is given by $x = (k/b^2)(1 - e^{-bt})$ where $b$ is a constant. What is the acceleration of the particle?

Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. Body $A$ moves with uniform acceleration $a$ and body $B$ moves with uniform velocity $V$. They meet after time $t$. The value of $t$ is

The distance $x$ covered in time $t$ by a body having initial velocity $u$ and having constant acceleration $a$ is given by $x=ut+\frac{1}{2}at^2$. This result follows from

The speeds of two identical cars are $u$ and $4u$ at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is