A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$$F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]$$

Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

A force $$\overrightarrow F = (40\widehat i + 10\widehat j)N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\overrightarrow r $$ at time t = 10 s, will be :

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s². The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____________ N. [Take g = 10 m/s² and $$\mu$$_s = 0.2]

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu$$_k. then, the block's acceleration 'a' is given by :

(g is acceleration due to gravity)