The correct option is A 163√23 m/s
We know that velocity is rate of change of position with respect to time, function of position is given as x=6+4t2–t4
∴Velocity, v=dxdt=8t−4t3
acceleration a=dvdt=8−12t2
For finding the maxima of any function we diffrentiate it and equate to zero.
⇒Velocity is maximum when dvdt=0
⇒8−12t2=0⇒t=√23
Now by substituting the time in the function of velocity we get,
maximum velocity,
=8√23−4.23.√23
=163√23 m/s
Hence option A is the correct answer