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The relation between position x and time t are given below for a particle moving along a straight line. Which of the following equations represent uniformly accelerated motion? {alpha and beta are positive constant}

The relation between position x and time t are given below for a particle moving along a straight line. Which of the following equations represent uniformly accelerated motion? {alpha and beta are positive constant}

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Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

For a uniformly accelerated motion, acceleration must be a constant.

In the forth option,

\alpha t=\sqrt{\beta +x}
\implies x=\alpha^2t^2-\beta
\implies v=\dfrac{dx}{dt}=2\alpha^2 t
\implies a=\dfrac{dv}{dt}=2\alpha^2 =constant
Hence option (4) is the answer.

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