Question

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.

Answer 1

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