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
With the help of a diagram, show the biasing of a light emitting diode (LED). Give its two benefits over conventional incandescent lamps.

what is virtual displacement?and how is it different from actual displacement?

The free surface of a liquid always has a tendency to contract and possess minimum surface area. If we want to enhance the surface area of the liquid, work has to be done. This wor

Define term practical optical fibre in short. Optical fibre: A practical optical fibre has in common three coaxial areas. The innermost area is the light guiding region term

Q. What are secondary cells? Give an example? i) They are rechargeable. ii) The chemical reactions which take place in secondary cells are reversible. iii) The active mat

working principle of a prism

Newtons law of inertia Truck and Ladder As per to Newton's first law, an object in motion continues within motion along with the similar speed and in the similar direction unle

a) What force is needed to give amass of 20kg an acceleration of 30m/s 2 ? b) Find the accelerating force when a car having a mass of 1.7Mg enhances its speed with a constant a

explain briefly about piezoelectric effect to produce ultrasonics

is pulling force easy or pushing