Position of a particle with time is given as x = t^3 - 3t^2. Instant when it turns back is t=? 

position x = t³ - 3t²  ;    velocity  ( dx/dt ) = 3t² - 6t

 

particle turning back means, velocity changes its sign

 

t	dx/dt
0	0
1	-3
2	0
3	9

 

As seen from the above table, velocity changes from -ve to +ve at  t= 2+ (immediately after t =2 )