Work when the force is increasing in relation to time

In summary, the work-energy theorem states that when the force is increasing in relation to time, the work W is equal to 1/2mu^2. This can be seen in the example where the acceleration of the mass increases by 1m/s^2 each second. The initial velocity is zero and the final velocity is u, with the mass remaining constant. This theorem is applicable in classical physics, not relativistic physics.
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Homework Statement



Is the work W equal to 1/2mu^2 when the force is increasing in relation to time? For example, the acceleration of the mass at the end of the 1st sec is 1meter/sec^2, at the end of the 2nd sec is 2meters/sec^2, at the end of the 3rd sec is 3meters/sec^2 and so on. The initial velocity of the mass is zero, and u is the final velocity of the mass. The mass remains constant. (classical physics, not relativistic).

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The Attempt at a Solution

 
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1. What is a force?

A force is a push or pull that can cause an object to accelerate or change direction.

2. How is work related to force and time?

Work is the product of force and displacement in the direction of the force. When the force is changing over time, the amount of work done will depend on the net force at each moment in time.

3. How does increasing force affect work?

Increasing force will result in an increase in the amount of work done, as long as the displacement remains constant.

4. What happens to work when force is increasing over time?

If the force is increasing at a constant rate, the work done will also increase at a constant rate. However, if the force is increasing at a non-constant rate, the work done will depend on the net force at each moment in time.

5. Are there any real-life examples of work being done when the force is increasing in relation to time?

Yes, there are many examples of this in everyday life. For instance, when lifting a heavy object, the force required will increase as the object is being lifted, resulting in an increase in work done. Similarly, when accelerating a car, the force applied to the gas pedal increases over time, resulting in an increase in work done to move the car forward.

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