3.1 Translational Kinetic Energy

• What is the formula for translational kinetic energy?

  $KE =$$\frac{1}{2} mv^{2}$
• What are the units for translational kinetic energy?

  Joules
• What is the role of integration in deriving the formula for translational kinetic energy?

  Calculating the work done
• Match the term with its formula:

  Kinetic Energy ↔️ $KE =$$\frac{1}{2} mv^{2}$

  Mass ↔️ $m$

  Speed ↔️ $v$
• The work-energy theorem states that the work done on an object equals the change in its kinetic energy.

  True
• In the formula for translational kinetic energy, the speed (v) is measured in meters per second.
• Mass is the measure of an object's resistance to acceleration.

  True
• A 2 kg object moving at 3 m/s has a kinetic energy of 9 J
• What is the formula for deriving the Joule in terms of mass and speed units?

  $1 \text{ J} =$$1 \text{ kg} \times (1 \text{ m / s})^{2}$
• Translational kinetic energy is the energy an object has because it's moving in a straight line, also known as translational
• Translational kinetic energy depends on an object's mass and speed.


  True
• The formula for translational kinetic energy can be derived by considering the work done to accelerate an object from rest to a final speed
• The work done on an object to accelerate it from rest equals its final kinetic energy.


  True
• What is the kinetic energy of a 2 kg ball moving at 3 m/s?

  9 Joules
• What is the formula for work done in terms of force and displacement?

  W = \int F \cdot dx</latex>
• Kinetic energy is the energy an object possesses due to its motion
• What is the unit of speed in the translational kinetic energy formula?

  Meters per second (m/s)
• The Joule is derived from the formula $1 \text{ J} =$$1 \text{ kg m}^{2} / \text{s}^{2}$


  True
• An object with a mass of 2 kg and a speed of 3 m/s has a kinetic energy of 9 J
• What is the translational kinetic energy of a 2 kg ball rolling at 3 m/s?

  9 J
• Steps in deriving the formula for translational kinetic energy:

  1️⃣ Start with the work-energy theorem

  2️⃣ Use force F = ma</latex> to rewrite the integral

  3️⃣ Change the variable of integration to velocity

  4️⃣ Integrate from 0 to $v$

  5️⃣ The result is $KE =$$\frac{1}{2} mv^{2}$
• Translational kinetic energy is the energy an object possesses due to its motion in a straight line
• The formula for work done is ∫F ⋅ dx
• The acceleration $a$ is equal to $dv / dt$


  True
• What is the final formula for work done when integrating from 0 to $v$?


  $W =$$\frac{1}{2} m v^{2}$
• Match the term with its formula:

  Kinetic Energy ↔️ $KE =$$\frac{1}{2} m v^{2}$

  Mass ↔️ $m$

  Speed ↔️ $v$
• A 2 kg object moving at 3 m/s has a kinetic energy of 9 J
• What is the kinetic energy of an object with a mass of 2 kg and a speed of 3 m/s?

  9 J
• A 2 kg ball rolls at 3 m/s. What is its kinetic energy?

  9 J
• If you double the speed of an object, its kinetic energy increases by a factor of four


  True
• Translational kinetic energy depends on an object's speed and mass.


  True
• The work-energy theorem states that the work done on an object equals the change in its kinetic energy
• What is the final formula for translational kinetic energy after integrating the work-energy theorem?

  $KE =$$\frac{1}{2} mv^{2}$
• What does the work-energy theorem state?

  Work equals change in KE
• If force F = ma, how can the work integral be rewritten?

  W = ∫ma ⋅ dx
• By changing the variable of integration to velocity, the work done can be expressed as ∫m ⋅ v ⋅ dv
• What is the formula for kinetic energy (KE)?

  $KE =$$\frac{1}{2} m v^{2}$
• What type of kinetic energy does the formula $KE =$$\frac{1}{2} m v^{2}$ represent?


  Translational kinetic energy
• The Joule (J) is equivalent to 1 kg m²/s²


  True
• Translational kinetic energy is calculated using the formula KE = \frac{1}{2} m v^2