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,

                        a = dv/dt                 dv = a dt

                        Integrating,  

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

                                              v = u + at                                                                     ...(i)

Further,           v = dx/dt    dx = vdt

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

Integrating within limits, equations change into,                 

 ...(ii)

Again, going back to definition of acceleration, we have,     a = dv/dt

Multiply and divide RHS of above equation by dx, equation gets,    

                                              a = v(dv/dx)   adv = adx

Integrating within limits, equation converts,             

                                              v2/2-u2/2 = a(s-0)    v2-u² = 2as                   ...(iii)

From (i) and (iii) we also result that,                                               ...(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 = at + 1/2at²;

v² - u² = 2as;

s = {(u+v)/2}*t

Email based Physics assignment help - homework help at Expertsmind

Are you searching physics expert for help with Equations of linear motion for Uniform Acceleration questions?  Equations of linear motion for Uniform Acceleration topic is not easier to learn without external help?  We at www.expertsmind.com offer finest service of Physics assignment help and physics homework help. Live tutors are available for 24x7 hours helping students in their Equations of linear motion for Uniform Acceleration related problems. We provide step by step Equations of linear motion for Uniform Acceleration question's answers with 100% plagiarism free content. We prepare quality content and notes for Equations of linear motion for Uniform Acceleration topic under physics theory and study material. These are avail for subscribed users and they can get advantages anytime.

Why Expertsmind for assignment help

1. Higher degree holder and experienced experts network
2. Punctuality and responsibility of work
3. Quality solution with 100% plagiarism free answers
4. Time on Delivery
5. Privacy of information and details
6. Excellence in solving physics queries in excels and word format.
7. Best tutoring assistance 24x7 hours