The correct option is C 4.5 m/s,3 m/s
Given, v(t)=t2−3t, we will check if the particle has changed its direction or not within the asked time interval, i.e. the time when velocity of the particle becomes zero.
⇒ t2−3t=0⇒ t=0,3 sec
Also, we know that
xf−xi=∫t0v(t)dt=∫t0(t2−3t)dt
⇒ xf−xi=t33−3t22
Let particle starts from origin i.e xi=0
So, at t=0,xf=0,
at t=3,xf=333−3×322=−92 m
at t=6,xf=633−3×622=18 m
So, the average speed of the particle is |−92|+|−92|+186=276=92=4.5 m/s
and, average velocity is 186=3 m/s