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## Homework Statement

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

a)

r''(t)→ = d^2/dt^2 [ ct^2 -2dt^3] i

a(t)→ = 2c - 12dt

t = (2c - a)/12d

b)

r"(t)→d^2/dt^2[ 2ct^2 - dt^3] j

a(t)→ = (4c -6dt)j

t = (4c - a)/6d

c)

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?