Understanding displacement and total distance traveled:

• If an object moves 4 m to the right and then 2 m to the left, its displacement is 2 m and the total distance traveled is 6 m.


  True
• What is the first step to apply displacement and total distance formulas in motion problems?

  Identify the velocity function
• Match the quantity with its description:

  Displacement ↔️ Change in position

  Total Distance Traveled ↔️ Absolute value of displacement
• The formula for total distance traveled using integration is |∫_{t_1}^{t_2} v(t) dt|
• What does a positive displacement indicate?

  Movement away from initial position
• Total distance traveled is the absolute value of the displacement
• What is the formula for displacement in terms of velocity and time?

  $\Delta x =$$\int_{t_{1}}^{t_{2}} v(t) \, dt$
• What is the formula for calculating displacement using integration?

  \Delta x = \int_{t_{1}}^{t_{2}} v(t) \, dt</latex>
• Match the variable with its meaning and units:

  \Delta x ↔️ Displacement in meters

  v(t) ↔️ Velocity function in m/s

  t_{1} ↔️ Initial time in seconds

  t_{2} ↔️ Final time in seconds
• What is the formula for calculating total distance traveled using integration?

  $|\Delta x| =$$|\int_{t_{1}}^{t_{2}} v(t) \, dt|$
• Displacement can be positive, negative, or zero
• Displacement has both magnitude and direction.

  True
• If an object moves from x=2 m to x=5 m and back to x=2 m, its displacement is zero.

  True
• Displacement can be positive, negative, or zero, while total distance traveled is always positive.


  True
• What is the key difference between displacement and total distance traveled?

  Direction and sign
• Displacement can be positive, negative, or zero, while total distance traveled is always positive.

  True
• Total distance traveled can be negative.

  False
• If a particle's velocity is v(t) = 2t</latex> m/s, its displacement between $t_{1} =$$1$ s and $t_{2} =$$3$ s is 8 meters.


  True
• What is the key difference between displacement and total distance traveled?

  Displacement can be negative
• What is the formula for total distance traveled?

  |\Delta x| = |\int_{t_{1}}^{t_{2}} v(t) dt|</latex>
• What is the formula for displacement using integration?

  $\Delta x =$$\int_{t_{1}}^{t_{2}} v(t) \, dt$
• What is the definition of displacement?

  Change in object's position
• The formula for displacement using integration is $\Delta x =$$\int_{t_{1}}^{t_{2}} v(t) dt$
• Total distance traveled is always a positive value.

  True
• What is the total length of the path an object has traveled called, regardless of direction?

  Total distance traveled
• The formula for total distance traveled is the absolute value of the displacement
• Displacement is a vector quantity with both magnitude and direction.
• How is total distance traveled related to displacement?

  Absolute value of displacement
• In the formula for displacement using integration, \Delta x represents the change in position.
• In the formula for total distance traveled using integration, the absolute value of the displacement is used.
• Displacement is a vector quantity that can be positive, negative, or zero.


  True
• What is the formula for displacement in physics?

  $\Delta x =$$\int_{t_{1}}^{t_{2}} v(t) dt$
• What type of quantity is displacement?

  Vector
• Total distance traveled is the absolute value of an object's displacement
• What is the key difference between displacement and total distance traveled?

  Direction
• Steps to calculate displacement and total distance traveled

  1️⃣ Identify the velocity function v(t)

  2️⃣ Integrate v(t) over the time interval [t₁, t₂] to find Δx

  3️⃣ Calculate the absolute value of Δx for total distance traveled
• In the displacement formula, Δx is measured in meters
• What is the formula for total distance traveled using integration?

  |\Delta x| = |\int_{t_{1}}^{t_{2}} v(t) dt|</latex>