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Thus, the work done for a variable force can be expressed as a definite integral of force over displacement. [24] If the displacement as a variable of time is given by ∆x(t), then work done by the variable force from t 1 to t 2 is:
When a force is applied on a spring, and the length of the spring changes by a differential amount dx, the work done is = For linear elastic springs, the displacement x is proportional to the force applied =, where K is the spring constant and has the unit of N/m.
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F ...
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The displacement of a body may be expressed in the form x = F(X), where X is the reference position of material points of the body; displacement has units of length and does not distinguish between rigid body motions (translations and rotations) and deformations (changes in shape and size) of the body. The spatial derivative of a uniform ...
The kinetic energy of an object is equal to the work, force times displacement , needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest. [2]
In contrast to an average velocity, referring to the overall motion in a finite time interval, the instantaneous velocity of an object describes the state of motion at a specific point in time. It is defined by letting the length of the time interval tend to zero, that is, the velocity is the time derivative of the displacement as a function of ...