3.18 Q: Kinematics

• What is the definition of displacement?

  Distance and direction of change
• What is acceleration defined as?

  Rate of change of velocity
• What type of motion is described when velocity remains constant?

  Constant velocity motion
• The units for velocity are m/s
• The magnitude of velocity is referred to as speed
• What variables does the equation $v^{2} =$$u^{2} +$$2as$ relate?


  Final velocity, initial velocity, acceleration, and displacement
• The equations of motion can only be used for objects moving under constant acceleration.


  True
• A car accelerates from rest at $2 m / s^{2}$ for 5 seconds. Its final velocity is 10 m / s
• Match the concept with its description:

  Displacement ↔️ Distance and direction of change in position

  Velocity ↔️ Rate of change of position with time
• Steps to solve kinematics problems using the equations of motion:

  1️⃣ Identify the known and unknown variables

  2️⃣ Choose the appropriate equation

  3️⃣ Substitute the known values

  4️⃣ Solve for the unknown variable
• The equation $v^{2} =$$u^{2} +$$2as$ relates final velocity squared to initial velocity squared, acceleration, and displacement
• Displacement refers to the distance and direction of an object's change in position
• Velocity is the derivative of displacement with respect to time.


  True
• What is the mathematical relationship between acceleration and velocity?

  $a(t) =$$\frac{dv(t)}{dt}$
• To find velocity from acceleration, you integrate the acceleration function with respect to time
• To find velocity from acceleration, you integrate the acceleration function with respect to time
• What is the formula for finding velocity from acceleration?

  $v(t) =$$\int a(t) dt$
• Given $v(t) =$$3t^{2} +$$2t$ and $s_{0} =$$5$, the displacement $s(t)$ is t^{3} + t^{2} + 5
• What type of quantity is velocity?

  Vector
• Match the equations of motion with their descriptions for constant velocity:

  $s =$$ut$ ↔️ Displacement equals initial velocity times time

  $v =$$u$ ↔️ Velocity remains constant
• Velocity is a vector quantity with both magnitude and direction
• Acceleration is a vector quantity.


  True
• One of the equations of motion is $v =$$u +$$at$, which relates final velocity, initial velocity, acceleration, and time
• To find velocity, you must integrate acceleration
• Match the concept with its definition:

  Displacement ↔️ Distance and direction of change

  Velocity ↔️ Rate of change of position
• Acceleration is a vector quantity.


  True
• What does the equation $v =$$u +$$at$ relate?


  Final velocity, initial velocity, acceleration, and time
• What is the first equation of motion that relates final velocity, initial velocity, acceleration, and time?

  $v =$$u +$$at$
• Match the equation of motion with its description:

  $v =$$u +$$at$ ↔️ Relates final velocity, initial velocity, acceleration, and time

  $s =$$ut +$$\frac{1}{2}at^{2}$ ↔️ Relates displacement, initial velocity, acceleration, and time

  $v^{2} =$$u^{2} +$$2as$ ↔️ Relates final velocity, initial velocity, acceleration, and displacement
• What is the mathematical relationship between velocity and displacement?

  $v(t) =$$\frac{ds(t)}{dt}$
• What is the definition of acceleration?

  Rate of change of velocity
• What is the formula relating final velocity, initial velocity, acceleration, and time under constant acceleration?

  $v =$$u +$$at$
• What type of problems are the equations of motion used to solve?

  Kinematics problems
• Match the concept with its description:

  Displacement ↔️ Change in position

  Velocity ↔️ Rate of change of displacement
• The derivative of velocity with respect to time gives acceleration.


  True
• What is the formula to calculate velocity from acceleration using integration?

  v(t) = \int a(t) dt</latex>
• If $a(t)$ is the acceleration function, $v(t) =$$\int a(t) dt$ gives the velocity.


  True
• Steps to find displacement from velocity

  1️⃣ Integrate the velocity function $v(t)$

  2️⃣ Add the constant of integration $C$

  3️⃣ Use initial conditions to find $C$
• What is the formula for finding displacement from velocity?

  s(t) = \int v(t) dt</latex>
• Match the concepts with their definitions:

  Displacement ↔️ The distance and direction of an object's change in position

  Velocity ↔️ The rate of change of an object's position with respect to time