3.2 Kinematics

• What is kinematics primarily concerned with?

  Motion of objects
• What is the relationship between acceleration and velocity in kinematics?

  \frac{dv}{dt} = a</latex>
• What is the relationship between acceleration and velocity in kinematics?

  $\frac{dv}{dt} =$$a$
• Velocity is the rate at which displacement changes over time.


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


  Final velocity
• Which formula relates final velocity, initial velocity, acceleration, and displacement?

  $v^{2} =$$u^{2} +$$2as$
• The constant acceleration formulas can be applied to objects with changing acceleration.

  False
• What does the slope of a displacement-time graph represent?

  Velocity
• Match the kinematic quantity with its definition:

  Position ↔️ Location of an object

  Velocity ↔️ Rate of change of position

  Acceleration ↔️ Rate of change of velocity
• Which formula relates final velocity, initial velocity, acceleration, and time?

  $v =$$u +$$at$
• What does the area under a velocity-time graph represent?

  Displacement
• The area under a velocity-time graph represents acceleration.

  False
• A straight line on a displacement-time graph indicates constant velocity.


  True
• Kinematics focuses on describing motion in terms of position, velocity, acceleration, and time
• Displacement refers to the change in position of an object.


  True
• What is the relationship between velocity and position in kinematics?

  $\frac{ds}{dt} =$$v$
• What are the constant acceleration formulas used to describe motion when acceleration is constant?

  Kinematic equations
• What does the formula $v^{2} =$$u^{2} +$$2as$ relate?


  Final velocity
• The constant acceleration formulas are used to analyze motion under constant acceleration.
• The area under a velocity-time graph represents the object's displacement.
• What is the relationship between displacement and velocity?

  $\frac{ds}{dt} =$$v$
• A car accelerating from rest to 30 m/s with a constant acceleration of 4 m/s² covers 112.5 meters in 7.5 seconds.


  True
• The area under a velocity-time graph represents displacement.


  True
• What does a straight line on a displacement-time graph indicate?

  Constant velocity
• The slope of a displacement-time graph represents velocity
• The slope of a displacement-time graph indicates velocity
• Match the graph type with its key feature:

  Displacement-Time ↔️ Slope

  Velocity-Time ↔️ Area under graph
• The formula v = u + at relates final velocity, initial velocity, acceleration, and time.


  True
• The slope of a displacement-time graph represents velocity
• A car traveling with constant acceleration covers a distance of 62.5 meters.
• What formula relates final velocity, initial velocity, acceleration, and displacement under constant acceleration?

  $v^{2} =$$u^{2} +$$2as$
• Vectors have both magnitude and direction.

  True
• What is the displacement of an object if its velocity is integrated over time?

  $s(t) =$$\int v(t) \, dt$
• Variable acceleration requires the use of calculus to analyze motion.


  True
• What is the relationship between displacement, velocity, and acceleration in kinematics?

  \frac{ds}{dt} = v, \frac{dv}{dt} = a</latex>
• Velocity is the rate of change of displacement with respect to time.


  True
• What is the average acceleration of a car that goes from rest to 25 m/s in 5 seconds?

  5 m/s²
• A ball accelerates from rest with a constant acceleration of 3 m/s² over 5 seconds. Its final velocity is 15 m/s.
• What does the area under a velocity-time graph represent?

  Displacement
• When solving motion problems with constant acceleration, the key is to use the constant acceleration formulas