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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?

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Solution

## 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:

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