The nucleus of a helium atom travels along the inside of a straight hollow tube $$4 \mathrm{~m}$$ long which forms part of a particle accelerator. If one assumes uniform acceleration, how long is the particle in the tube if it enters at a speed of $$2000 \mathrm{~m} / \mathrm{s}$$ and leaves at $$8000 \mathrm{~m} / \mathrm{s}$$

A drone is flying due west, a little above the train, with a speed of $$10 \mathrm{~m} / \mathrm{s}$$. A 270 meter long train is moving due east at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. The time taken by the drone to cross the train is

The displacement $$x$$ of a particle in a straight line motion is given by $$x=1-t-t^2$$. The correct representation of the motion is

Two guns P and Q can fire bullets at speeds 2 km/s and 4 km/s, respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum or areas covered by the bullets fired by the two guns, on the ground is