Question

the position of a particle will respect to time T along y axis is given by Y =12t^2-2t^3, where why is in metre and T is in seconds full stop when the particle achieve maximum speed the position of particle would be

Answer 1

this the solution you want.

Answer 2

Answer:

The particle achieve maximum speed the position of particle would be 32 m.

Explanation:

Given that,

The position is

$y = 12t^2-2t^3$

The velocity is the first derivative of the particle.

$v = \dfrac{dy}{dt}=24t-6t^2$

The maximum speed is

$\dfrac{dv}{dt}=24-12t$

$\dfrac{dv}{dt}=0$

$24-12t=0$

$t = 2\ sec$

So, the speed will be maximum at t = 2 sec

So, the displacement at t = 2 is given by

$Y=12\times(2)^2-2\times(2)^3$

$Y = 32\ m$

Hence, The particle achieve maximum speed the position of particle would be 32 m.