Engineering Mechanics example (Gate-2005)

Que: A time variation of the position of a particle in rectilinear motion is given by  x = 2t3 + t2 + 2t  If v is the velocity and a is the acceleration of particle in constant units, the motion started with (Gate-2005)

(a) v = 0, a = 0
(b) v = 0, a = 2
(c) v = 2, a = 0
(d) v = 2, a = 2

Ans: (d)
Explanation: 
x = 2t3 + t2 + 2t  So,
Velocity v = dx/dt = 6t2 + 2t +2
Acceleration  a = 12t + 2

At the start of motion  t = 0, Then
v =  0 + 0 + 2 = 2
a = 0 + 2 = 2