The position '$$x$$' of a particle varies with a time as $$x=a t^2-b t^3$$ where '$$a$$' and '$$b$$' are constants. The acceleration of the particle will be zero at

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

A small steel ball is dropped from a height of $$1.5 \mathrm{~m}$$ into a glycerine jar. The ball reaches the bottom of the jar $$1.5 \mathrm{~s}$$ after it was dropped. If the retardation is $$2.66 \mathrm{~m} / \mathrm{s}^2$$, the height of the glycerine in the jar is about (acceleration due to gravity $$g=9.8 \mathrm{~m} / \mathrm{s}^2$$ )

A large number of bullets are fired in all directions with same speed '$$U$$'. The maximum area on the ground on which the bullets will spread is