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 = \[\left| \frac{d x}{d t} \right|_{t = 0}\]

\[\frac{d x}{d t} = u + 2a(t - 2s)\]

\[\left| \frac{d x}{d t} \right|_{t = 0} = u - 4\text{ as } \neq u\]

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)