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STAR GIRL
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In equation K= ∫mvdv = ∫m dx/dt dv, how can we write v at any time t as dx/dt?? Does it make any sense??
This is how velocity is defined. How do you define velocity?STAR GIRL said:In equation K= ∫mvdv = ∫m dx/dt dv, how can we write v at any time t as dx/dt?? Does it make any sense??
I just want to know that how can we write v as dx/dtfresh_42 said:This is how velocity is defined. How do you define velocity?
Yup I got it. ThanksIbix said:Well, velocity is the rate of change of position (x) with respect to time (t). So v=dx/dt by definition.
K is the symbol for kinetic energy, which is the energy an object possesses due to its motion. The integral symbol, ∫, represents the mathematical operation of integration. The letter m represents mass, v represents velocity, and t represents time. Therefore, the equation is a representation of the relationship between kinetic energy and the mass, velocity, and time of an object.
The equation is derived from the fundamental principles of classical mechanics, specifically the work-energy theorem. It states that the work done on an object is equal to the change in its kinetic energy. Using calculus and the definition of work, the equation K= ∫Fdx is transformed into K= ∫mvdv = ∫m dx/dt dv.
The unit of measurement for kinetic energy is joules (J). Mass is measured in kilograms (kg), velocity in meters per second (m/s), and time in seconds (s). Therefore, the units for the equation are J = kg*m^2/s^2.
The equation is used in various fields, such as physics, engineering, and chemistry, to calculate the kinetic energy of objects. It is also used to analyze and predict the motion of objects and systems, such as projectiles, particles, and molecules. Additionally, the equation is used in the development and design of machines and devices that utilize kinetic energy.
Yes, the equation can be applied to all objects as long as their mass, velocity, and time are known or can be measured. However, in certain cases, such as for objects with non-uniform velocity, rotational motion, or relativistic speeds, the equation may need to be modified or other equations may be more suitable.