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Questions  

An object moves with constant acceleration a. Which of the following expressions is/are also constant? 

a
d|v→|dt
b
dv→dt
c
dv2dt
d
d(v→/|v→|)dt

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 vzall 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+vz2×2vxdvxst+2vydvyst+2vzdvzst=v→⋅a→vwhich is a variable quantity.dv→dt=|a→|, which would be constant. dv2dt=dvx2+vy2+vz2dt=2v→⋅a→        (a variable quantiry)d(v→/v)dt=ddtvxi^+vyj^+vzk^vx2+vy2+vz2        (a variable quantiry)

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