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Question

If the position vector of a point P relative to the origin varies with time as, r=2αt ^iβ t2^j , where α and β are constants, then the equation for trajectory of the particle is

A
y=βx24α2
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B
y=βx22α2
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C
y=βx22α
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D
y=βx24α
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Solution

The correct option is A y=βx24α2
Given,
r=2αt^iβt2^j=x^i+y^j
then,
x=2αtt=x2α
and y=βt2y=βx24α2

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