If the position vector of a point P relative to the origin varies with time as, →r=2αt^i−βt2^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 Ay=−βx24α2 Given, →r=2αt^i−βt2^j=x^i+y^j then, x=2αt⇒t=x2α and y=−βt2⇒y=−βx24α2