A particle moves along a straight line such that its position `x` at any time t is `x = 3r^2 - t^3`, where `x` is in metre and t in second , them, Options: A . &nbspat t = 0 acceleratiom is 6 m /`s^2` B . &nbsp`x - t` curve has maximum at 8 m C . &nbsp`x - t` curve has maximum at 2 s D . &nbspboth (A) and (B) are correct.

Answer: Option D (A) The given expression is `x = 3t^2 - t^3` `v = (dx)/(dt) = 6t - 3t^2` `a = (dv)/(dt) = 6 - 6t` At ` t = 0, a = 6 m/s^2` Hence , (a) is correct , (C) For maximum of `x - t` curve, `(dx)/(dt) = 0` `:.` `6t - 3t^2 = 0` `:.` t = 2 sec. Hence , (C) is correct. Hence , finally (D) is correct.

A particle moves along

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Question -

A particle moves along a straight line such that its position `x` at any time t is `x = 3r^2 - t^3`, where `x` is in metre and t in second , them,

Options:

A . at t = 0 acceleratiom is 6 m /`s^2`

B . `x - t` curve has maximum at 8 m

C . `x - t` curve has maximum at 2 s

D . both (A) and (B) are correct.

Answer: Option D

(A) The given expression is `x = 3t^2 - t^3`

`v = (dx)/(dt) = 6t - 3t^2`

`a = (dv)/(dt) = 6 - 6t`

At ` t = 0, a = 6 m/s^2`

Hence , (a) is correct ,

`(dx)/(dt) = 0`

`:.` `6t - 3t^2 = 0`

`:.` t = 2 sec.

Hence , (C) is correct.

Hence , finally (D) is correct.

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