Understanding displacement and total distance traveled:

    Cards (86)

    • Unlike total distance traveled, displacement can be positive or negative.
      True
    • Total distance traveled is always a non-negative value.
    • Match the concept with its definition or calculation:
      Displacement ↔️ Final Position - Initial Position
      Total Distance Traveled ↔️ ∫|v(t)| dt from t₁ to t₂
    • What is the key difference between displacement and total distance traveled?
      Direction
    • What is the formula for velocity in terms of position?
      v(t)=v(t) =dxdt \frac{dx}{dt}
    • Velocity can be positive or negative, indicating the direction of movement.

      True
    • Match the concept with its definition:
      Velocity ↔️ Rate of change of position
      Displacement ↔️ Change in position
    • Unlike total distance traveled, displacement can be positive or negative
    • What is the definition of total distance traveled?
      Total length of path covered
    • If a particle's velocity is v(t) = 2t - 4, the total distance traveled from t = 0 to 3 is calculated by integrating |2t - 4|.

      True
    • What is the definition of speed?
      Rate of covering distance
    • How is displacement calculated using a velocity function?
      ∫v(t)dt\int v(t) dt
    • Velocity is a vector quantity, meaning it has both magnitude and direction
    • The displacement of a particle with velocity v(t) = 3t² - 6t + 2 from t = 0 to t = 3 is 6 units.

      True
    • Steps to calculate total distance traveled using integration
      1️⃣ Identify the velocity function
      2️⃣ Calculate the absolute value of the velocity function
      3️⃣ Set the integration limits
      4️⃣ Integrate the absolute value over the time interval
      5️⃣ Evaluate the integral
    • What is the formula for calculating displacement?
      Final Position - Initial Position
    • To calculate the total distance traveled, we integrate the absolute value of the velocity
    • Displacement is calculated as the final position minus the initial position.
    • What is the mathematical formula for velocity in terms of position x(t)x(t)?

      v(t)=v(t) =dxdt \frac{dx}{dt}
    • If a car moves forward 50 meters in 5 seconds, its velocity is 10 m/s.

      True
    • What is the formula for calculating speed?
      \text{Speed} = \frac{\text{Total Distance Traveled}}{\text{Time Taken}}\)</latex>
    • If v(t)=v(t) =3t2−6t+ 3t^{2} - 6t +2 2, its displacement from t=t =0 0 to t=t =3 3 is 6 units.
    • Displacement indicates direction from start to finish.

      True
    • To calculate the total distance traveled using a speed function, we integrate the absolute value of the velocity
    • Steps to calculate total distance traveled using a velocity function
      1️⃣ Identify the velocity function
      2️⃣ Calculate the absolute value of the velocity
      3️⃣ Define the integration limits
      4️⃣ Compute the definite integral
      5️⃣ Evaluate the integral
    • What is the total distance traveled for \( v(t) = 3t^2 - 6t \) from \( t = 0 \) to \( t = 3 \)?
      8 units
    • Total distance traveled is calculated by integrating the absolute value of the velocity
    • What is always true about the total distance traveled?
      It is always non-negative
    • What is displacement defined as?
      Change in position
    • Match the concept with its definition or calculation:
      Displacement ↔️ Change in position from start to finish
      Total Distance Traveled ↔️ Total length of path covered
    • How is total distance traveled calculated?
      ∫|v(t)| dt from t₁ to t₂
    • If a car starts at position 5 meters and ends at position 15 meters, what is its displacement?
      10 meters
    • If a car moves 10 meters forward and then 5 meters back, its displacement is 5 meters.

      True
    • Velocity is a vector quantity that considers both magnitude and direction.

      True
    • Velocity is a vector quantity that considers both magnitude and direction
    • A velocity of 10 m/s indicates that an object is moving forward at a rate of 10 meters per second.

      True
    • Arrange the concepts in order from simplest to most complex in terms of calculation:
      1️⃣ Displacement
      2️⃣ Total Distance Traveled
    • To calculate total distance traveled, we integrate the absolute value of the velocity function over a given time interval
    • What is the key difference between displacement and total distance traveled?
      Direction and path
    • Unlike velocity, speed is a scalar quantity.
      True