Equations of linear motion for uniform acceleration, Physics

Given a particle moving along a straight line with fixed acceleration a. Let u be the initial velocity of the particle and v be the velocity at time t. So by definition,

                                                                              2065_linear motion.png               dv = a dt

                        Integrating, 479_linear motion1.png

(a being a constant may be taken out of the integral)                 v - u = at

                                           v = u + at                                                                     ...(i)

 

Further,  2361_linear motion2.png           dx = vdt

 

But,      v = u + at,               dx = (u + at)dt

 

Integrating within limits, equations change into,  949_linear motion3.png               

 

2249_linear motion4.png

                                                                                                          ...(ii)

Again, going back to definition of acceleration, we have,    306_linear motion5.png

Multiply and divide RHS of above equation by dx, equation gets,   406_linear motion6.png 

                                      1540_linear motion7.png      adv = adx

Integrating within limits, equation converts,      1709_linear motion8.png            →    291_linear motion9.png   

1370_linear motion10.png      →          1166_linear motion11.png

                                                                       ...(iii)

From (i) and (iii) we also result that,   2162_linear motion12.png                                       ...(iv)

Equation (iv) is a special equation, as we do not have a in this equation, but still it belongs to motion, which is uniformly accelerated.

To result, we again write the equation of motion for constant acceleration below.

v = u + at ;     s = ut + 557_linear motion13.png1395_linear motion14.png       695_linear motion15.png      

Posted Date: 8/3/2012 3:19:14 AM | Location : United States







Related Discussions:- Equations of linear motion for uniform acceleration, Assignment Help, Ask Question on Equations of linear motion for uniform acceleration, Get Answer, Expert's Help, Equations of linear motion for uniform acceleration Discussions

Write discussion on Equations of linear motion for uniform acceleration
Your posts are moderated
Related Questions
Color vision and chromatic aberration: One of the remarkable ability of the eye is its ability to see color. There are three types of cones that respond to light from three

Q. Explain what do you understand by the terms potential well and potential barrier. How does a particle with energy lesser than the barrier height tunnels through its quantum mech

why can one ignore quantization of charge when dealing with macroscopic charges

Newton's law of universal gravitation (Sir I. Newton): Two bodies attract  to each other with equal & opposite forces; the magnitude of this force is proportional to the produ

im trying to build an electric motor and would like to know y they wind there copper wire in what paturn to make power and secondly what is the output per gram of copper in these t


Electromagnetic waves: Electromagnetic waves with different ranges of frequency constitute an electromagnetic spectrum. Electromagnetic waves are transverse in nature. Visible

Newton 2nd law of motion proof

Infrared radiations and Ultra Violet radiations: What are infrared radiations and Ultra Violet radiations? Ans: Infrared: Wavelengths larger than visible light 2. Wav

What makes a flashlight suddenly become dim or bright when you shake it?