1.2 Displacement, Velocity, and Acceleration

• Distance traveled is a scalar quantity with both magnitude and direction.

  False
• What is instantaneous velocity calculated as in calculus?

  \frac{dx}{dt}</latex>
• Acceleration is the rate at which velocity changes over time
• Match the feature with the correct quantity:

  Change in position ↔️ Displacement

  Total path length ↔️ Distance Traveled
• Instantaneous velocity is the velocity at a specific moment in time.


  True
• Acceleration is a vector quantity that indicates both magnitude and direction.


  True
• Velocity is the rate of change of displacement over time.


  True
• A car starts at rest and accelerates at 3 m/s² for 4 seconds. What is its velocity after 4 seconds?

  12 m/s
• A person walks 5 meters east and then 3 meters west. What is their displacement?

  2 m east
• What is the definition of velocity?

  How fast an object is moving and in what direction
• Instantaneous velocity is calculated as the limit of $\frac{\Delta x}{\Delta t}$ as $\Delta t$ approaches zero.


  True
• Match the type of acceleration with its description:

  Average acceleration ↔️ Change in velocity over a time interval

  Instantaneous acceleration ↔️ Acceleration at a specific moment
• What is the relationship between acceleration and velocity?

  Acceleration is the rate of change of velocity
• The kinematic equations are used to solve problems involving constant acceleration.

  True
• Steps to solve a kinematics problem:

  1️⃣ Identify the known variables

  2️⃣ Choose the appropriate kinematic equation

  3️⃣ Substitute the known variables into the equation

  4️⃣ Solve for the unknown variable
• A person walks 5 meters east and then 3 meters west. What is their displacement?

  2 meters east
• Instantaneous velocity reflects the actual speed at a specific moment.


  True
• Instantaneous acceleration is the limit of average acceleration as the time interval approaches infinity.

  False
• How is average velocity defined mathematically?

  $v_{avg} =$$\frac{\Delta x}{\Delta t}$
• Instantaneous velocity is calculated as the limit of \(\frac{\Delta x}{\Delta t}\)
• The formula for average acceleration is \(\frac{\Delta v}{\Delta t}\)
• Acceleration is the rate of change of velocity
• Displacement is a vector quantity with both magnitude and direction.


  True
• Velocity is a vector quantity that includes both speed and direction.


  True
• Velocity is a vector quantity, meaning it has both magnitude and direction
• What is the definition of acceleration?

  The rate at which velocity changes over time
• Instantaneous acceleration is calculated as the limit of $\frac{\Delta v}{\Delta t}$ as $\Delta t$ approaches zero.


  True
• The units of acceleration are meters per second squared
• Which kinematic equation relates final velocity, initial velocity, acceleration, and time?

  $v_{f} =$$v_{i} +$$at$
• Displacement is the change in the position
• Average velocity is defined as the change in displacement divided by the change in time
• If a car travels 100 meters in 5 seconds, what is its average velocity?

  20 m/s
• A car increases its velocity from 10 m/s to 30 m/s in 5 seconds. What is its average acceleration?

  4 m/s²
• The average velocity formula is \(\frac{x_f - x_i}{t_f - t_i}\)
• What is the average velocity of a car that travels 100 meters in 5 seconds?

  20 m/s
• A car increases its velocity from 10 m/s to 30 m/s in 5 seconds. What is its average acceleration?

  4 m/s²
• Match the quantity with its definition:

  Displacement ↔️ Change in position

  Velocity ↔️ Rate of change of displacement

  Acceleration ↔️ Rate of change of velocity
• Distance traveled is a scalar quantity with only magnitude and no direction.
• A car travels 100 meters in 5 seconds. What is its average velocity?

  20 m/s
• Match the type of velocity with its description:

  Average velocity ↔️ Total displacement divided by time interval

  Instantaneous velocity ↔️ Velocity at a specific moment