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A particle moves along the x-axis and has its displacement x varying with time t according to the equation \(\mathrm{x}=…

Q1

A particle moves along the x-axis and has its displacement x varying with time t according to the equation \(\mathrm{x}={\mathrm{c}}_{0}\left({\mathrm{t}}^{2}-2\right)+\mathrm{c}(\mathrm{t}-2{)}^{2}\) where \({\mathrm{c}}_{0}\) and c are constants of appropriate dimensions. Then, which of the following statements is correct?

[JEE Main 2025, 3 Apr (Shift 2)]

a

the acceleration of the particle is \(2{\mathrm{c}}_{0}\)

b

the acceleration of the particle is \(2\mathrm{c}\)

c

the initial velocity of the particle is \(4\mathrm{c}\)

d

the acceleration of the particle is \(2\left(c+{c}_{0}\right)\)

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