If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $$v\left( x \right) = \beta {x^{ - 2n}}$$, where $$\beta $$ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = $$\sqrt x + 3$$. The displacement of the particle when its velocity is zero, will be

A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃ is