Rectilinear Motion Concepts

Rectilinear Motion Concepts

• Rectilinear motion describes the movement of an object along a straight line.
• Key variables include displacement, distance, velocity, speed, acceleration, and time.
• Displacement is the change in position of an object, a vector quantity.
• Distance is the total path length traveled, a scalar quantity.
• Velocity is the rate of change of displacement, a vector quantity.
• Speed is the rate of change of distance, a scalar quantity.
• Acceleration is the rate of change of velocity, a vector quantity.
• Time is the duration of the motion.

Equations of Motion (Constant Acceleration)

• These equations describe the relationship between the variables in rectilinear motion when acceleration is constant.
• The most common equations are:
  • v = u + at (final velocity equals initial velocity plus acceleration times time)
  • s = ut + ½at² (displacement equals initial velocity times time plus half acceleration times time squared)
  • v² = u² + 2as (final velocity squared equals initial velocity squared plus 2 times acceleration times displacement)
  • s = (v + u)/2 * t (displacement equals average velocity times time)
• These equations apply to situations with uniform acceleration such as:
  • Objects falling under gravity (neglecting air resistance).
  • Objects moving on a frictionless surface with a constant applied force
• These equations are simplified models, and if the acceleration is not constant, more complex solutions are required.

Graphical Representations

• Position-time graphs:
  • The slope of the graph represents velocity.
  • A horizontal line indicates zero velocity.
  • A steeper line represents higher velocity.
• Velocity-time graphs:
  • The slope of the graph represents acceleration.
  • A horizontal line indicates constant velocity (zero acceleration).
  • A positive slope represents positive acceleration.
• Acceleration-time graphs:
  • The area under the graph represents the change in velocity.
  • A horizontal line represents constant acceleration.

Uniform Motion

• Uniform motion is a special case of rectilinear motion where the velocity is constant.
• In uniform motion acceleration is zero (a=0).
• The equations simplify to:
  • v = u (constant velocity)
  • s = vt (displacement equals velocity times time)

Non-Uniform Motion

• When acceleration is not constant, the equations of motion for uniform acceleration do not apply.
• More sophisticated calculus methods might be needed to analyze the motion.

Free Fall

• Free fall is a special case of rectilinear motion where the only acceleration is due to gravity.
• The acceleration due to gravity (often represented by 'g') is approximately 9.8 m/s² near the Earth's surface.
• The equations of motion can be applied to free fall problems, using acceleration 'g' instead of 'a'.

Distance vs Displacement

• Distance is a scalar quantity and measures the total path length covered.
• Displacement is a vector quantity and measures the straight-line change in position.
• In the simplest rectilinear motion cases, they could be the same but it depends on the path.

Problem Solving Strategies

• Identify the known variables.
• Identify the unknown variables.
• Choose the appropriate equation of motion.
• Substitute the known values into the equation.
• Solve for the unknown variable.
• Check if the answer is reasonable and in line with given units.