A particle moves along x -axis as x=4(t-2)+a(t-2)^2 . Which of following statements is true?

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2.Motion in Straight Line

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A particle moves along $x$-axis as $x=4(t-2)+a(t-2)^2$. Which of the following statements is true?

A

The initial velocity of particle is $4$

B

The acceleration of particle is $2\,a$

C

The particle is at origin at $t=0$

D

None of the above

Solution

(b)

$x=4(t-2)+a(t-2)^2$

At $t=0, x=-8+4 a=4 a-8$

$v=\frac{d x}{d t}=4+2 a(t-2)$

At $t=0, \quad v=4-4 a=4(1-a)$

But acceleration, $\frac{d^2 x}{d t^2}=2 a$

Standard 11

Physics

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