The displacement of a particle undergoing rectilinear motion along x-axis is given by X=2t3+21t2+60t+6 where X is in meter And - Physics - Kinematics

Question

The displacement of a particle undergoing rectilinear motion along
x-axis is given by X=2t​3+21t2+60t+6
where X is in meter And t is in second find the acceleration of the
particle when its velocity is zero ?

Ved Prakash Lakhera · Accepted Answer

Given      X=2t3+21t2+60t+6So     dXdt=6t2+42t+60When velocity is zero then dXdt=0or      6t2+42t+60=0or        6t2+12t+30t+60=0or           6tt+2+30t+2=0or           t=-2s, -5sNow  differentiating the given eqn once again, we get;       d2Xdt2=12t+42So accelerations at time t=-2s and t=-5s is given by;             d2Xdt2=12×-2+42=-24+42=18m/s2and          d2Xdt2=12-5+42=-60+42=-18m/s2

The displacement of a particle undergoing rectilinear motion along x-axis is given by X=2t​3+21t2+60t+6 where X is in meter And t is in second . find the acceleration of the particle when its velocity is zero ?

The displacement of a particle undergoing rectilinear motion along x-axis is given by X=2t³+21t²+60t+6 where X is in meter And t is in second . find the acceleration of the particle when its velocity is zero ?