Question

The position x of a particle at any time t is given by
x=6-12t+4t²
Calculate the maximum velocity of the particle

Answer 1

Explanation:

$x = 4 {t}^{2} - 12t + 6 \\ \frac{dx}{dt} = v = 8t - 12 \\ we \: have \: to \: find \: maximum \: velocity \: so \\ take \: </p><p>[tex] \frac{dv}{dt} = 0 \\ 8 = 0$

since we can't find dv/dt so we can't find its max. and min. values

Answer 2

x=6-12t+4t²

we know that

v=dx/dt

=-12+8t

max velocity is at dv/dt=0

8=0

as this isn't possible therefore its max velocity isn't defined.

(though by observation u can say it as infinity but infinity isn't defined ans doesn't exist)