If displacement #S# of an article is given by #S=at^2-bt^3#, then when is it moving at uniform velocity?

1 Answer
May 30, 2017

Acceleration is #2a-3bt# and it is zero when #t=a/(3b)#

Explanation:

When displacement #S=S(t)# of a article is a function of #t#, its velocity #v(t)=(dS)/(dt)# and its acceleration #a=(d^2S)/(dt^2)#

As #S=at^2-bt^3#

we have #v(t)=2at-3bt^2#

and #a(t)=2a-6bt#

As such acceleration is #2a-6bt#

and acceleration is zero i.e. uniform velocity

when #2a-6bt=0# or #t=(2a)/(6b)=a/(3b)#