Engineering dynamics question The motion of a particle is de

Engineering dynamics question: The motion of a particle is defined by the relation x = t^3 – 9t^2 + 24t – 8, where x and t are expressed in inches and seconds, respectively. Determine the time when the velocity is zero. (Round the final answer to the nearest whole number.)

The magnitudes of time when the velocity is zero are:

Solution

given distance traveled in function of time

we know that velocity is the change in displacement.

given   x = t^3 – 9t^2 + 24t - 8

dx/dt = 3t²-18t+24

V = 3t²-18t+24

t=? when V=0

3t²-18t+24 = 0

(t-4) (t-2) =0

t = 4 and t=2

the magnitudes of time when velocity is 0