A particle is moving along the Y -axis. The position of the particle from the origin as a function of time (t) is given as y(t)=10 t e^ -2 t . How far is the particle from the origin when it stops momentarily? ( y is given in units of metre and t is in units of second)

Step-by-step solution

The position of the particle is given as y(t)=10 t e^ -2 t (i) Velocity of the particle is given as v= d d t y(t)= d d t (10 t e^ -2 t )=10 [t e^ -2 t (-2)+e^ -2 t 1 ]=10 [-2 t e^ -2 t +e^ -2 t ]=10 e^ -2 t (1-2 t) When body stops, then v=0 e^ -2 t (1-2 t)=0 1-2 t=0t= 1 2 ~s From Eq. (i), displacement of the particle from origin is given as y ( 1 2 )=10 1 2 e^ -2 1 2 =5 e⁻¹= 5 e ~m