Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{~ms}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{-1}$$ is __________.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : When a body is projected at an angle $$45^{\circ}$$, it's range is maximum.

Reason R : For maximum range, the value of $$\sin 2 \theta$$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

An object moves with speed $$v_1,v_2$$ and $$v_3$$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be: