(i) v = \(\frac{dx_A}{dt}\,=\,2\)
and a = \(\frac{d^2x_A}{dt^2}\) = 0
as per this eqn. the particle has no acceleration at all.
(ii) v = \(\frac{dx_B}{dt}\)
= 3 × 2t + 2 + 0
= 6t + 2
a = \(\frac{d^2 x_B}{dt^2}\)
Here, acceleration is uniform.
(iii) v = \(\frac{dx_c}{dt}\)
= 5 × 3t2 + 4
= 15t2 + 4
a = \(\frac{dv}{dt}=\frac{d_2x_c}{dt^2}\)
= 15 × 2t = 30t
Here, acceleration depend upon time so it is not uniform.