The displacement is given as S=t5−40t3+80t−25 V=
dS
dt
=5t4−120t2+60t+80 a=
d2S
dt2
=20t3−240t+60 Let, a=f(t)=20t3−240t+60 f′(t)=60t2−240 Put f′(t)=0 60t2=240 t=±2 At t=2f′(t)>0 Therefore, the minimum value of acceleration is amin=f(2)=20(2)3−240(2)+60 =−260
