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Lady_Fox [76]
3 years ago
6

A particle moves along a straight line and its position at time t is given by

Physics
1 answer:
Alisiya [41]3 years ago
3 0

(A) Use interval notation to indicate the time interval or union of time intervals when the particle is moving forward and backward

the particle is speeding up

<span>if  a(t) >0, it means 12t-48>0, and t >4,  I = ]4, infinity[</span>

the particle is speeding down

<span>if  a(t) < 0, it means 12t-48>0, and t < 4,  I = ] -infinity, 4[</span>

 

when the particle is moving forward and backward

that is depending of the sign of v(t)

moving forward if v(t)> 0

<span>moving backward if v(t)<  0</span>

but v(t) = 6t² - 48 t +90, this quadratic equation has exactly two solutions, t =1, and t =3

<span>so  after taking care the sign of </span>6t² - 48 t +90,

 

<span>v(t)> o when  t is in I = ] –inf, 1[ U ]4, inf[,the particle is moving forward</span>

<span>v(t) < o when  t is in I = ]1, 4[,the particle is moving backward</span>

<span> </span>

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