A 0.55-kg particle has a speed of 5.0 m/s at point A and kinetic energy of 7.6 J at point B. a. What is its kinetic energy at A?
b. What is its speed at point B?
c. What is the total work done on the particle as it moves from A to B?

(a) The kinetic energy at A is 6.875 J.

(b) The speed at point B is 5.26 m/s.

(c) The total work done on the particle as it moves from A to B is 0.725 J.

Explanation:

Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and at rest, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless a change in speed occurs or the body returns to its state of rest by applying a force.

Kinetic energy is represented by the following formula:

Ec = ½ *m*v²

Where Ec is kinetic energy, which is measured in Joules (J), m is mass measured in kilograms (kg), and v is velocity measured in meters over seconds (m/s).

(a) In this case, you know:

Replacing:

Ec = ½ *0.55 kg*(5 m/s)²

and solving you get:

Ec= 6.875 J

The kinetic energy at A is 6.875 J.

(b) In this case, you know:

Replacing:

7.6 J = ½ *0.55 kg*v²

and solving you get:

v= 5.26 m/s

The speed at point B is 5.26 m/s.

(c)  The total work done on the particle as it moves from A to B is the difference between the work done at the end point (point B) and the work done at the start point (point A). Considering that work is equal to kinetic energy, then:

Work= Ec at point B - Ec al point A= 7.6 J - 6.875 J

Work= 0.725 J

The total work done on the particle as it moves from A to B is 0.725 J.

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