If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y=5 x(1-x)$$. The $$y$$ component vector of the initial velocity is ______________ $$\hat{j}$$. ($$\mathrm{Take}$$ $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$
A particle is moving in a straight line such that its velocity is increasing at 5 ms$$-$$1 per meter. The acceleration of the particle is _____________ ms$$-$$2 at a point where its velocity is 20 ms$$-$$1.
A car is moving with speed of $$150 \mathrm{~km} / \mathrm{h}$$ and after applying the break it will move $$27 \mathrm{~m}$$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___________ m distance.
A car covers AB distance with first one-third at velocity v1 ms$$-$$1, second one-third at v2 ms$$-$$1 and last one-third at v3 ms$$-$$1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms$$-$$1 then the average velocity of the car is _____________ ms$$-$$1.