A particle's position is r =(ct^2−2dt^3) i hat+(2ct^2−dt^3)j hat. where c and d are positive constants.
part a) Find expressions for times t > 0 when the particle is moving in the x-direction.
part b) Find expressions for times t > 0 when the particle is moving in the y-direction.
Is there any time,t >0 when the particle is c) at rest and d) accelerating in the x-direction?
If either answer us "yes", find the time(s).
The Attempt at a Solution
r''(t)→ = d^2/dt^2 [ ct^2 -2dt^3] i
a(t)→ = 2c - 12dt
t = (2c - a)/12d
r"(t)→d^2/dt^2[ 2ct^2 - dt^3] j
a(t)→ = (4c -6dt)j
t = (4c - a)/6d
If particle is at rest, then velocity = 0
v→ = r'(t)→ = (2ct - 6dt^2) i + (4ct - 3dt^2) j
0 = (2ct - 6dt^2) i + (4ct - 3dt^2) j
how do I proceed from here?