The 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 the acceleration of the particle in consistent units, the motion started with
v=2,a=2
Given:
x=2t3+t2+2t
Velocity: V=dxdt=6t2+2t+2
At t=0 (start of motion)
V=0+0+2
V=2
Acceleration: a=dvdt=12t+2
At t=0
a=0+2
∴a=2