The time variation of the position of a particle in rectilinear motion is given by $$x = 2{t^3} + {t^2} + 2t$$. If 'V' is the velocity and 'a' acceleration of the particle in consistent units, the motion started with

A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5m/s. the net force on the bob at the mean position is

The figure shows a pin-jointed plane truss loaded at the point M by hanging a mass of 100 kg. The member LN of the truss is subjected to a load of v

A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance ‘s’ along the floor. Assuming $$\mu $$ to be the coefficient to kinetic friction between the block and the floor and ‘g’ the acceleration due to gravity what is the velocity v of the bullet?