Question

The position x of a particle with respect to time t along x -axis is given by x=9t^2-t^3, where x is in metre and t in second. What will be the position of this particle when it achieves maximum speed along the position x-direction?

Answer 1

Here is your answer...

Answer 2

Answer:

x = 54 m

Explanation:

It is given that,

The position x of a particle with respect to time t along x -axis is given by :

$x=9t^2-t^3$ .....(1)

Where,  x is in metre and t in second

We need to find the position of this particle when it achieves maximum speed along the position x-direction.

Velocity v of the particle is given by :

$v=\dfrac{dx}{dt}\\\\v=\dfrac{d(9t^2-t^3)}{dt}\\\\v=18t-3t^2$

For maximum speed, $\dfrac{dv}{dt}=0$

So,

$\dfrac{dv}{dt}=\dfrac{d}{dt}(18t-3t^2)\\\\18-6t=0\\\\t=3\ s$

Put t = 3 s in equation (1) such that :

$x=9(3)^2-(3)^3\\\\x=54\ m$

So, the position of this particle at maximum speed is 54 m.