Kinetic energy as a function of time

In summary, kinetic energy as a function of time is a mathematical representation of the relationship between the movement of an object and the energy it possesses. It is calculated using the formula KE = 1/2 * m * v^2 and is affected by the mass and velocity of the object. It is a form of mechanical energy that can be converted into other forms and can also be negative when the velocity or object's speed is negative.
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Homework Statement
a particle of mass m is subjected to a force F=F°(cos(t)i+sin(t)j) if initially the particle was at rest the kinetic energy of the particle as a function of time is fgiven by
Relevant Equations
a=dv/dt
I got acceleration by dividing force by m then replaced a by dv/dt and then integrated it to get velocity as a fxn of time and hence got kinetic energy but problem is my ans does not match with any option can someone please compare their ans
 

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  • #2
Can you show us what you did?
 
  • #3
PeroK said:
Can you show us what you did?
 

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  • #4
What velocity do you get at ##t=0##?
 
  • #5
PeroK said:
What velocity do you get at ##t=0##?
Ya i got my mistake and got the ans thanks
 
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1. What is kinetic energy as a function of time?

Kinetic energy as a function of time refers to the mathematical relationship between an object's kinetic energy and the amount of time it takes to reach a certain velocity. It describes how the energy of an object changes over time as it moves.

2. How is kinetic energy as a function of time calculated?

The formula for calculating kinetic energy as a function of time is KE = 1/2mv2, where KE is kinetic energy, m is the mass of the object, and v is the velocity.

3. What factors affect kinetic energy as a function of time?

The two main factors that affect kinetic energy as a function of time are mass and velocity. Generally, the greater the mass and velocity of an object, the greater its kinetic energy will be. Other factors that can affect kinetic energy include air resistance, friction, and the presence of external forces.

4. Why is kinetic energy as a function of time important in science?

Kinetic energy as a function of time is important in science because it helps us understand the motion and behavior of objects. By studying how kinetic energy changes over time, we can make predictions about an object's speed, acceleration, and other physical properties.

5. How is kinetic energy as a function of time related to potential energy?

Kinetic energy and potential energy are two forms of energy that are constantly changing and converting between each other. As an object moves, its potential energy decreases and its kinetic energy increases. This relationship is described by the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

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