The velocity of a subatomic particle moving through space ca

The velocity of a subatomic particle moving through space can be modeled by v(t) = 0.1 tr^2 - 7.2t + 0.1 for t greaterthanorequalto 0 where t is time in seconds and v is velocity in m/s. Find the following: (a) The time(s) t at which the particle is not moving. (b) The interval(s) over which the particle is moving forward.

Solution

given velocity ,v(t)=0.1t²-7.2t+0.1

a)

when partical is not moving ,v(t)=0

=>0.1t²-7.2t+0.1=0

=>t²-72t+1=0

=>t²-72t=-1

=>t²-72t+36²=-1+36²

=>(t-36)²=1295

=>(t-36)=-1295,(t-36)=1295

=>t=36-1295,t=36+1295

partical is not moving when t=36-1295 and 36+1295

partical is not moving when t=0.01 and 71.99

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(b)

when partical is moving forward ,v(t)>0

0.1t²-7.2t+0.1>0

=>t²-72t+1>0

=>t²-72t>-1

=>t²-72t+36²>-1+36²

=>(t-36)²>1295

=>(t-36)<-1295,(t-36)>1295

=>t<36-1295,t>36+1295

=>t (0,0.01)U(71.99,)

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(b)

when partical is moving backward ,v(t)<0

0.1t²-7.2t+0.1<0

=>t²-72t+1<0

=>t²-72t<-1

=>t²-72t+36²<-1+36²

=>(t-36)²<1295

=>-1295<(t-36)<1295

=>36-1295<t<36+1295

=>t (0.01,71.99)