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
He chemical effects of electricity

working principle of vibration and deflection magnetometer?

Fusion Reaction: In nuclear fusion light nuclei are brought together to form a relation heavier nucleus. They energy free in nuclear fusion is larger than that free in fission.

The microwave (rotational) spectrum of 12 C 16 O having  a series of lines spaced by 115.3 GHz. Suppose that the rotational  energy levels of this molecule can be approximated by


Q. What is an optical fibre and dispersion? Write the expression for angle of deviation.

Resolution of Forces by Calculation: One vector was resolved into two mutually perpendicular components. So if there are several vectors each can be resolved into two

Actually vectors are divisible but not directly. A vector is multiplied by the inverse of the vector to be divided.In other way, its magnitude an be divided and multiplied by a uni

Alpha particles are nuclei of: a) Hydrogen b) Helium c) Oxygen d) Nitrogen Ans: Alpha particles are nuclei of helium.

5 example of Classification and 5 types of Vectors and 3 Dimensional Forces