Question

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?

Answer 1

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: