A ball is projected vertically upwards from ground. It reaches a height '$$h$$' in time $$t_1$$, continues its motion and then takes a time $$t_2$$ to reach ground. The height $h$ in terms of $$g, t_1$$ and $$\mathrm{t}_2$$ is $$(\mathrm{g}=$$ acceleration due to gravity)

Two cars A and B start from a point at the same time in a straight line and their positions are represented by $$\mathrm{R}_{\mathrm{A}}(\mathrm{t})=$$ at $$+\mathrm{bt}^2$$ and $$\mathrm{R}_{\mathrm{B}}(\mathrm{t})=x \mathrm{t}-\mathrm{t}^2$$. At what time do the cars have same velocity?

A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm{V} / 2$$' when it penetrates $$30 \mathrm{~cm}$$ in a target. Through what thickness it will penetrate further in the target before coming to rest?

Two trains, each $$30 \mathrm{~m}$$ long are travelling in opposite directions with velocities $$5 \mathrm{~m} / \mathrm{s}$$ and $$10 \mathrm{~m} / \mathrm{s}$$. They will cross after