Question

A 600 kg car is at rest, and then accelerates to 5 m/s. What is its original kinetic energy? J What is its final kinetic energy? J How much work was used? J

Answer 1

1) Original kinetic energy: 0

The kinetic energy of an object is given by:

$K=\frac{1}{2}mv^2$

where m is the mass of the object and v the speed of the object.

In this problem, the mass of the car is m=600 kg, but its initial speed is zero (it is at rest), so v=0 and Ki=0.

2) Final kinetic energy: 7,500 J

Using again the formula for the kinetic energy:

$K=\frac{1}{2}mv^2$

And using the mass of the car (m=600 kg) and its final speed (v=5 m/s), we find

$K_f=\frac{1}{2}(600 kg)(5 m/s)^2 =7,500 J$

3) Work used: 7,500 J

The kinetic energy theorem states that the work done on an object is equal to its gain in kinetic energy:

$W=K_f -K_i$

Using the kinetic energies found in the previous points, we find the work done

$W=7,500 J-0 = 7,500 J$

Answer 2

Taking into account the definition of kinetic energy and work, yo get:

• The original kinetic energy is 0 J.
• The final kinetic energy is 7500 J.
• The work used is 7500 J.

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.

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

Kinetic energy is represented by the following formula:

Ec = ½ mv²

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).

• Original kinetic energy

In this case, a 600 kg car is at rest (it means that v=0 m/s). Its original kinetic energy can be calculated as:

Ec = ½ (600 kg)× (0 m/s)²

Solving:

Ec= 0 J

The original kinetic energy is 0 J.

• Final kinetic energy

Then, the 600 kg car accelerates to 5 m/s. Its final kinetic energy can be calculated as:

Ec = ½ (600 kg)× (5 m/s)²

Solving:

Ec= 7500 J

The final kinetic energy is 7500 J.

• Work

The kinetic energy theorem states that the work done by the applied net force (sum of all forces) is equal to the change in kinetic energy:

Work= Ec final - Ec original

In this case, knowing the Ec final and original:

Work= 7500 J - O J

Solving

Work= 7500 J

The work used is 7500 J.

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