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Question

# An object moves velocity →v having constant accelaration →a. Which of the following expressions are variable quantities ?

A
d|v|dt
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B
∣ ∣dvdt∣ ∣
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C
d(|v|2)dt
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D
dv|v|dt
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Solution

## The correct option is D d⎛⎜⎝→v−→|v|⎞⎟⎠dtlet →v=vx^i+vy^j+vz^k and →a=ax^i+ay^j+az^k=dvxdt^i+dvydt^j+dvzdt^k 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 , then corresponding velocity component may be constant.) A) |→v|=√v2x+v2y+v2z Hence d|→v|dtis variable. ∴Option(a) is correct. B) By definition d→vdt=→a hence d→vdt is constant ∴Option(b) is incorrect. C) |→v|2=v2x+v2y+v2z d|→v|2dt is variable ∴Option(c) is correct. D) d⎛⎜⎝→v−→|v|⎞⎟⎠dt=d⎛⎜ ⎜⎝vx^i+vy^j+vz^k√v2x+v2y+v2z⎞⎟ ⎟⎠dt is variable quantity. ∴Option(d) is correct.

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