A particle's position is r⃗ = (ct2-2dt3) i^ + (2ct2-dt3) j^,

where c and d are positive constants. Find expressions for times t > 0 when the particle is moving in the x-direction.

If we are concern only with the velocity of the particle along the x-axis, then, this implies that the velocity along the y-axis is hypothetically = 0ms^-1

∴ v = (vx=0, vy)

vy = 0ms^-1

vy = (dr/dt) y = 0ms^-1

ry→ = (2ct^2 - dt^3) j

dr/dt = 4ct - 3dt^2

4ct - 3dt^2 = 0

4c = 3dt

t = 4c/3d