Question

The position of a particle with respect to time t along y-axis is given by: y=12t^2-2t^3, where, y is in metres and t is in seconds. When the particle achieves maximum speed, the position of the particle would be?

Answer 1

ur answer is in attachment

Answer 2

Answer : The particle will have maximum speed at t = 2 s and it is at 32 m.

Explanation :

The position of the particle is given by :

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

We know that $v=\dfrac{dy}{dt}$

So,

$v=\dfrac{d}{dt}(12t^2-2t^3)$

$v=24t-6t^2$

We have to maximize speed i.e. $\dfrac{dv}{dt}=0$

$24-12t=0$

$t=2\s$

So, the position of particle at t = 2 s will be :

$y=12(2)^2-2(2)^3$

$y=32\ m$

Hence, this is the required solution.