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The motion of a particle is defined by the relationx = 6t4 − 2t3 −12t2 + 3t + 3, where x and t are expressed in meters and seconds, respectively. Determine the time, the position, and the velocity when a = 0. |
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Answer» Answer: t = 2/3 sec x = 0.25925 meters v = -8.5555 meters/sec Step-by-step EXPLANATION: The motion of a particle is: x = 6t4 − 2t3 −12t2 + 3t + 3 Differentiate with respect to TIME we get, velocity=24t3 - 6t2 - 24t + 3 Again, Differentiate with respect to time we get, acceleration = 72t2 - 12t - 24 according to question, a=0 ⇒ 72t2 - 12t -24 = 0 ⇒ (2t+1)*(3t-2) = 0 ⇒ t= -1/2 OR t = 2/3 ∵ time is not NEGATIVE ∴ time, t=2/3 sec put this time value in position and velocity equation we get, position, x = 0.25925 meters and Velocity, v = -8.5555 meters/sec |
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