An object moves with constant acceleration a→. Which of the following expressions is/are also constant?
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a
d|v→|dt
b
dv→dt
c
dv2dt
d
d(v→/|v→|)dt
answer is B.
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Detailed Solution
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)