1.The position vector of a particle is given as r?=(t2-4t+6)î+(t2)j.The time after which the velocity vector and accleration vector becomes perpendicular to each other is equal to

never

 

v = dr/dt = (2t-4)i +(2t)j       v = velocity

a = 2i+2j                          a = acceleration

 

for a and v to be perpendicular,

=>  a.v = 0           . is dot product

=>   (2i+2j).[(2t-4)i+(2t)j] = 0

=>     4t -8 +4t = 0

=>     8t =8 

i.e t=1 

A block of mass M is moving on a smooth horizontal surface with constant speed u. Bullets arefired horizontally against the block to reduce the velocity of the block to half its initial value.Bullets get embedded in the block. Mass of each bullet is ‘m’ and speed ‘u’. Then the number ofbullets required is–