A particle starts from the origin at t = 0 s with a velocity of and moves in the x-y plane with a constant acceleration of .

(a) At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?

(b) What is the speed of the particle at the time?

Velocity of the particle,

Acceleration of the particle

Also,

But,

Integrating both sides:

Where,

= Velocity vector of the particle at t = 0

= Velocity vector of the particle at time t

Integrating the equations with the conditions: at t = 0; r = 0 and at t = t; r = r

Since the motion of the particle is confined to the x-y plane, on equating the coefficients of , we get:

(a) When x = 16 m:

∴y = 10 × 2 + (2)² = 24 m

(b) Velocity of the particle is given by: