An object moves with constant acceleration $\overrightarrow{\mathrm{a}}$. Which of the following expressions is/are also constant?

detailed solution

Correct option is B

Let a→=axi^+ayj^+azk^=dvxdti^+dvydtj^+dvzdtk^As a→ is constant, so its magnitude as well as direction is not changing, but vx,vy and vz all can be varying (any combination of these if  ax,ay or az=0, then corresponding velocity component may be constant).|v→|=v=vx2+vy2+vz2d|v→|dt=12vx2+vy2+vz2×2vxdvxdt+2vydvydt+2vzdvzdt=v→⋅a→vwhich is a variable quantity.dv→dt=|a→|, which would be constant.dv2dt=dvx2+vy2+vz2dt=2v→⋅a→   (a variable quantity) d(v→/v)dt=ddtvxi^+vyj^+vzk^vx2+vy2+vz2    (a variable quantity)