Question

How much kinetic energy does the block now gain as it moves a distance of 2 m?

Answer 1

B) 14 J

Step-by-step explanation

Kinetic energy is a form of energy that an object or a particle has by reason of its motion and its mass, it is given by the expression:

`\begin{gathered} E_k=(1)/(2)mv^2^{} \\ \text{where} \\ E_k\text{ is the kinetickenergy} \\ m\text{ is the mass} \\ v\text{ is the velocity} \end{gathered}`

also, work is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.

it is given by:

`\begin{gathered} W=F\cdot d \\ \text{Wis the work done} \\ \text{F is the force } \\ d\text{ is the distance} \end{gathered}`

Step 1

find the work 1

Let

`\begin{gathered} m=\text{ 5 }kg \\ F_1=\text{ 5N} \\ \end{gathered}`

replace

`\begin{gathered} W=5kg\cdot\text{ 5N} \\ W=\text{ 25 Joules} \end{gathered}`

Step 2

find the work 2

Let

`\begin{gathered} m=\text{ 5 }kg \\ F_2=\text{12N} \\ \end{gathered}`

replace

`\begin{gathered} W=5kg\cdot\text{ 12N} \\ W=\text{ 60 Joules} \end{gathered}`

Step 3

now, the difference of force and the distance will give us the increase of kinetick energy

`\begin{gathered} \Delta K=F_(net)\cdot\Delta dis\tan ace \\ \Delta K=(12N-5N)(2m) \\ \Delta K=7\text{ N}\cdot2\text{ m} \\ \Delta K=14\text{ Joules} \end{gathered}`

since the box had a 5N force acting on it before it jumped to 12 N,it only acts to the / N difference

therefore, the answer is

B) 14 J