A particle moves in a straight line so that t seconds after passing through a fixed point O its velocity V m/s is given by the equation V=20t-2t^2 m/s.find the initial acceleration of the particle, the value of t when the particle is at rest?

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Answer 1 · 2017-08-30T10:53:54

initial acceleration#" "20ms^(-2)#

particle at rest when# t=0s, 10s#

we are given

#v=20t-2t^2----(1)#

#(1)" "#when the particle is at rest

ie when #v=0#

taking #(1)# we have

#20t-2t^2=0#

#t(20-2t)=0#

#=>t=0" or "#

#20-2t=0=>t=10#

particle at rest when# t=0s, 10s#

#(2)" "#initial accelaration

acceleration is calculated by #(dv)/(dt)#

differentiating #(1)#

#v=20t-2t^2#

#(dv)/(dt)=20-4t#

#[(dv)/(dt)]_(t=0)=20-4xx0=20ms^(-2)#