A particle moves along a straight line. The acceleration of particle as function of time is given by a = 6 t − 12 . Initial velocity of particle is 9 m / s and distance traveled by particle in 5 sec i

Question

A particle moves along a straight line. The acceleration of particle as function of time is given by a = 6 t − 12 . Initial velocity of particle is 9 m / s and distance traveled by particle in 5 sec is 7 x (in m ). Find the value of x .

TestHub · Accepted Answer

a = 6 t − 12 ∫ 9 v ​ d v = ∫ 0 t ​ ( 6 t − 12 ) d t v − 9 = 3 t 2 − 12 t v = 3 t 2 − 12 t + 9 v = 0 at t = 1& t = 3 S = ​ ∫ 0 1 ​ ( 3 t 2 − 12 t + 9 ) d t ​ + ​ ∫ 1 3 ​ ( 3 t 2 − 12 t + 9 ) d t ​ + ​ ∫ 3 5 ​ ( 3 t 2 − 12 t + 9 ) ​ d t S = 28 m

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