   Chapter 12.3, Problem 56E

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# Particle Motion Consider a particle moving on an elliptical path described by r ( t ) = a cos ω t i + b sin ω t j where ω = d θ / d t is the constant angular speed.(a) Find the velocity vector. What is the speed of the particle?(b) Find the acceleration vector and show that its direction is always toward the center of the ellipse.

(a)

To determine

To calculate: The speed, velocity vector of the particle if a particle moving on an elliptical path r(t)=acosωti +bsinωtj where ω=dθ/dt constant angular speed.

Explanation

Given:

A particle moving on an elliptical path r(t)=acosωti +bsinωtj where ω=dθ/dt constant angular speed.

Formula used:

The velocity vector is v(t)= r(t) and Magnitude of velocity gives speed which is v(t).

Calculation:

Consider the position vector,

r(t)=acosωti +bsinωtj

(b)

To determine

To calculate: The acceleration vector and then show its direction is always towards center if a particle moving on an elliptical path r(t)=acosωti +bsinωtj where ω=dθ/dt constant angular speed.

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