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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 dv|v|dt
let 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
dvdt=a
hence dvdt is constant

Option(b) is incorrect.

C)
|v|2=v2x+v2y+v2z
d|v|2dt is variable
Option(c) is correct.

D)
dv|v|dt=d⎜ ⎜vx^i+vy^j+vz^kv2x+v2y+v2z⎟ ⎟dt is variable quantity.


Option(d) is correct.




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