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Q.

A particle moves along the X-axis as $x = u (t - 2) + a {(t - 2)}^{2}$
a) the initial velocity of the particle is u

b) the acceleration of the particle is a

c) the acceleration of the particle is 2a

d) at t = 2 s particle is at the origin

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a

c & d are correct

b

b & c are correct

c

a & c are correct

d

a & b are correct

answer is D.

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Detailed Solution

x = u (t - 2) + a {(t - 2)}^{2}

$B .S .diff .w .r .to't'$

$v = \frac{d x}{dt} = \frac{d}{dt} [u (t - 2) + a {(t - 2)}^{2}]$

$= \frac{d}{dt} (u (t - 2)) + \frac{ad}{dt} (t^{2} - 4 t + 4)$

$= u + a [2 t - 4]$

$a = \frac{dv}{dt} = 0 + 2 a$

$∴ a = 2a$

$t = 2 s^{1}$

$x = u (2 - 2) + a {(2 - 2)}^{2}$

$x = 0$

particle is at the origin

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