Question

The motion of a particle is defined by the relation
x = 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.

Answer 1

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