For a train engine moving with speed of $$20 \mathrm{~ms}^{-1}$$, the driver must apply brakes at a distance of 500 $$\mathrm{m}$$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $$\sqrt{x} \mathrm{~ms}^{-1}$$. The value of $$x$$ is ____________.

(Assuming same retardation is produced by brakes)

A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was travelled with speed $$10 \mathrm{~m} / \mathrm{s}$$ for half the time and with speed $$15 \mathrm{~m} / \mathrm{s}$$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $$\frac{x}{7} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ is ___________.

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms$$^{-2}$$.

(Given g = 10 ms$$^{-2}$$)

A ball is thrown vertically upwards with a velocity of $$19.6 \mathrm{~ms}^{-1}$$ from the top of a tower. The ball strikes the ground after $$6 \mathrm{~s}$$. The height from the ground up to which the ball can rise will be $$\left(\frac{k}{5}\right) \mathrm{m}$$. The value of $$\mathrm{k}$$ is __________. (use $$\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$$)