a particle starts at time t = 0 and moves along the x - axis so that its position at any time t is greater than or equal to zero is given x(t) = (t-1)^3(2t-3)

Question

A. Find the velocity of the particle at any time t greater than or equal to 0.
B. For what values of t is the velocity of the particle less than zero.
C. Find the value t when the particle is moving and the acceleration is 0.

Answer 1

v(t) = dx/dt = (t-1)^2 (8t-11)

v<0 when 8t-11<0

a(t) = 3/8 ((8t-9)^2 - 1), so a=0 when
(8t-9)^2 = 1
8t-9 = ±1
8t = 8 or 10
t = 1 or 5/4
but at t=1, v=0, so t=5/4 is the answer.