The position vector of a particle is given by the relation `vecr=vecalpha(1-gammat+betat^(2))`, where `vecalpha` is a constant vector while, `beta` and `gamma` are positive constants. Which of the following statement is true ?

Options

A. Displacement in first two seconds is `vecalpha(1-2gamma+4beta)`
B. Velocity at `t=0` is `-vecalphagamma`.
C. Acceleration at `t=0` is `2betavecalpha`.
D. Speed is decreasing with time at `t=0`.

Explanation

To solve the problem, we need to analyze the position vector of the particle given by:

\[ \vec{r} = \vec{\alpha}(1 - \gamma t + \beta t^2) \]

where \(\vec{\alpha}\) is a constant vector, and \(\beta\) and \(\gamma\) are positive constants. We will evaluate the statements provided in the question.

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