10. Derive all Formullas of Non Uniform Velocity.
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Answer:
A very important issue related to your question is that Newton's kinematical equations are valid only when a particle is having uniform acceleration in one dimensional motion. For multidimensional motion ,it may be resolved into suitable components. And then the kinematical equations maybe applied for each component. Now, coming back to the main stream answer, the term “equation of motion” is a bit confusing. But still consider a problem through which I am willing to answer your question. Obtain the velocity of a particle that started from rest and whose non uniform acceleration varies with time as a=2kt, k is a constant. Starting to solve this problem the first thing to note is that dv/dt=2kt=a, separating the variables, dv= 2ktdt, integrating both sides, V= kt^2 +C, C is the constant of integration. To evaluate C the initial condition is used. This implies that C= 0, V= kt^2. (Because the particle started from rest,at t=0, V=0).One can perform another round of integration to find the position of the particle as a function of time. If it's this that you wanted to know, I believe that you will understand it through this example. But,if it's not so, ask your question again being careful about the idea that you want to convey. If you request me to answer, I will try to do so as soon as I can.
Explanation:
Example of uniform motion: A body moving with a constant speed in a straight line has uniform motion. Non-uniform motion: When an object covers an unequal distance in equal interval of time, the motion is called non-uniform motion.