# NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 8

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Question 4.21:

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:

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

But,

Integrating the equations with the conditions:

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

We get:

And,

(a) When x = 16 m:

(b) Velocity of the particle is given by:

Speed of the particle: