**8. An Application to Mechanics**A particle \( x(t) \) of mass \( 1 \, \text{kg} \) is moving along a horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force \( F(t) = g \). Knowing that the particle was initially at the origin, with negative speed \(-v_0\), find the expression of \( x(t) \) in terms of \( g \) and \( v_0 \) and find the position further on the left where the particle will be. Finally, find the expression of the time \( T \) when the particle will be back at the origin.

Write the expression of x(t) at time t in terms of g and vo. xt=vit+12at2Here, Ft=g=mag=1aa=g, thenxt=-v0t+12gt2At the final velocity, vf=0 then,vf=vi+at0=-v0+gtt=v0gthen,xt=-v0v0g+12gv0g2x(t)=-v022g Write the expression of time T when the particle will be back again at the origin. In forward,vf=-v0+gt10=-v0+gt1t1=v0gIn backward,v0=0+gt2t2=v0gso, T=t1+t2T=2v0g

Engineering

Mechanical Engineering

A particule x(t) of mass 1kg is moving along an horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force F(t) = g. Knowing that the particle what initially at the origin, with negative speed -vo, find the expression of x(t) time t in terms of g and u and find the position further on the left where the particule will be. Finally, find the expression of the time T when the particle will be back at the origin.

A particule x(t) of mass 1kg is moving along an horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force F(t) = g. Knowing that the particle what initially at the origin, with negative speed -vo, find the expression of x(t) time t in terms of g and u and find the position further on the left where the particule will be. Finally, find the expression of the time T when the particle will be back at the origin.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**8. An Application to Mechanics**

A particle \( x(t) \) of mass \( 1 \, \text{kg} \) is moving along a horizontal straight line (positively oriented on the right). The particle is under the effect of a positive constant force \( F(t) = g \). Knowing that the particle was initially at the origin, with negative speed \(-v_0\), find the expression of \( x(t) \) in terms of \( g \) and \( v_0 \) and find the position further on the left where the particle will be. Finally, find the expression of the time \( T \) when the particle will be back at the origin.

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