Question

The position of a particle moving along x-axis given by x= (-2t^3 + 3t^2 + 5)m. the acceleration of particle at the instant itd velocity becomes zero is

Answer 1

Please find below the answer

Answer 2

To find out acceleration with the given data of position in three dimension, we need to write them 3D equation of motion and then differentiate with respect to time to attain velocity and then input the given data in order to attain answer.

Given is $x=-2{ t }^{ 2 }+3t+5$. By differentiating it with respect to time, we get $v=\frac { dx }{ dt } =-6{ t }^{ 2 }+6t$.

Given situation is when velocity is zero. Input v = 0. $\Rightarrow 0=-6{ t }^{ 2 }+6t \Rightarrow 0 = t (-6t+6) \Rightarrow$ either t be 0 or 1.

Further differentiate the given equation to attain acceleration.  

$a=\frac { dv }{ dt } =-12t+6;$ if t = 0,

then a = 6;

and if t=1,

then a = -6