The position of a particle is given by s= f(t)=t^3-6t^2+9 where t is in seconds and s in meters ? a) when is the particle moving backward ( that is in the negative direction)? b) FInd the acceleration at time t and after 4s?
1 Answer
May 27, 2018
Position of a particle with respect to time is given as
#s= f(t)=t^3-6t^2+9#
(a) Particle will move backwards when its velocity is negative
#=>v(t)=dots=d/dt(t^3-6t^2+9)#
#=>3t^2-12t#
Imposing given condition we get
#3t^2-12t<0#
Solutions is
#0" > "t" < "4\s#
(b) Acceleration
#=>a(t)=d/dt(3t^2-12t)#
#=>a(t)=6t-12#
Also#a_4=6xx4-12=12\ ms^-2#
