The displacement (x) of a particle depends on | vedclass

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(D) The displacement is given by $x = \alpha t^2 - \beta t^3$.$1$. To check if the particle returns to its starting point,set $x = 0$:$\alpha t^2 - \b

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$(a)$ and $(c)$ only

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(D) The displacement is given by $x = \alpha t^2 - \beta t^3$.$1$. To check if the particle returns to its starting point,set $x = 0$:$\alpha t^2 - \beta t^3 = 0 \implies t^2(\alpha - \beta t) = 0$.This gives $t = 0$ and $t = \frac{\alpha}{\beta}$. Since the particle returns to $x = 0$ at $t = \frac{\alpha}{\beta}$,statement $(a)$ is incorrect.$2$. Velocity $v = \frac{dx}{dt} = 2\alpha t - 3\beta t^2$. Setting $v = 0$ for rest:$t(2\alpha - 3\beta t) = 0 \implies t = 0$ or $t = \frac{2\alpha}{3\beta}$. Thus,statement $(b)$ is correct.$3$. Acceleration $a = \frac{dv}{dt} = 2\alpha - 6\beta t$. At $t = 0$,$a = 2\alpha$. Since $2\alpha 
eq 0$,the initial acceleration is not zero. Thus,statement $(c)$ is incorrect.Since both $(a)$ and $(c)$ are incorrect,the correct choice is $(d)$.

The displacement $(x)$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$. Choose the incorrect statements from the following.

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