The motion of a particle is defined by the relation x = 2t3 - 9t2 + 12t + 10 , where x and t are expressed in feet and seconds , respectively . Determine the time , the position , and the acceleration of the particle when v = 0 ?

1 )  The motion of a particle is defined by the relation x = 2t3 - 9t2 + 12t + 10 , where x and t are expressed in feet and seconds , respectively .  Determine the time , the position , and the acceleration of the particle when v = 0 ?

A )  t = 1 s    ,     x = 15 ft    ,    a = 6 ft / s2   And

t = 2 s    ,     x = 14 ft    ,     a = 6 ft / s2   .

B )  t = 3 s   ,    x = 15 ft    ,     a = 8 ft / s2    And

 t = 5 s  ,     x = 14 ft   ,     a = 12 ft / s2 .

C )   t = 2 s   ,     x = 15 ft   ,     a = 9 ft / s2     And

t = 4 s   ,     x = 14 ft    ,     a = 7 ft / s2  .

Correct Answer : -   A )  t = 1 s    ,     x = 15 ft    ,    a = 6 ft / s2   And

t = 2 s    ,     x = 14 ft    ,     a = 6 ft / s2   .

Solution : -

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2 )  During a parasailing ride ,  the boat is traveling at a constant 30 km / hr with a 200 m long tow line . At the instant shown ,  the angle between the line and the water is 30° and is increasing at a constant rate of 2°/s .  Determine the velocity and acceleration of the parasailer at this instant .

A )  vp = 13.280 m / s       ,          a = 0.2437  m / s2  .

B )   vp = 11.280 m / s        ,         a = 9.2437  m / s2 .

C )   vp = 12.280 m / s       ,          a = 8.2437  m / s2  .

Correct Answer : -   A )  vp = 13.280 m / s   ,   a = 0.2437  m / s2  .

Solution : -

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