Question

A particle moves along the X-axis as
x = u (t − 2 s) + a (t − 2 s)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.

Answer 1

(c) the acceleration of the particle is 2a
(d) at t = 2 s, the particle is at the origin

Initial velocity = ${\left|\frac{dx}{dt}\right|}_{t=0}$
$\frac{dx}{dt}=u+2a(t-2s)$
${\left|\frac{dx}{dt}\right|}_{t=0}=u-4as\ne u$

Acceleration =$\frac{d^{2}x}{d{t}^2}=2a$
At t = 2 s,
x = u(2 s − 2 s) + a (2 s − 2 s)² = 0 (origin)