1D Motion Kinematics: Displacement, Distance, Speed, and Velocity

1D Motion Kinematics

Displacement and Distance

• Displacement: change in position of an object from initial to final position ( scalar quantity)
• Distance: total length of path traveled by an object (scalar quantity)
• Displacement can be negative, distance is always positive

Speed and Velocity

• Speed: rate of change of distance with respect to time (scalar quantity)
• Velocity: rate of change of displacement with respect to time (vector quantity)
• Speed is always positive, velocity can be negative

Acceleration

• Acceleration: rate of change of velocity with respect to time (vector quantity)
• Can be positive (increasing velocity) or negative (decreasing velocity)

Equations of Motion

• v = u + at: final velocity (v) equals initial velocity (u) plus acceleration (a) times time (t)
• s = ut + (1/2)at^2: displacement (s) equals initial velocity (u) times time (t) plus half of acceleration (a) times time (t) squared
• v^2 = u^2 + 2as: final velocity (v) squared equals initial velocity (u) squared plus two times acceleration (a) times displacement (s)

Graphical Analysis

• Position-time graph: shows displacement vs. time
• Velocity-time graph: shows velocity vs. time
• Acceleration-time graph: shows acceleration vs. time
• Slope of position-time graph gives velocity
• Slope of velocity-time graph gives acceleration

1D Motion Kinematics

Displacement and Distance

• Displacement is the change in position of an object from its initial to final position, and it's a scalar quantity.
• Distance is the total length of the path traveled by an object, and it's also a scalar quantity.
• A key difference between displacement and distance is that displacement can be negative, but distance is always positive.

Speed and Velocity

• Speed is the rate of change of distance with respect to time, and it's a scalar quantity.
• Velocity is the rate of change of displacement with respect to time, and it's a vector quantity.
• Speed is always positive, but velocity can be negative, depending on the direction of motion.

Acceleration

• Acceleration is the rate of change of velocity with respect to time, and it's a vector quantity.
• Acceleration can be either positive (indicating increasing velocity) or negative (indicating decreasing velocity).

Equations of Motion

• The equation v = u + at relates an object's final velocity (v) to its initial velocity (u), acceleration (a), and time (t).
• The equation s = ut + (1/2)at^2 relates an object's displacement (s) to its initial velocity (u), time (t), and acceleration (a).
• The equation v^2 = u^2 + 2as relates an object's final velocity (v) to its initial velocity (u), acceleration (a), and displacement (s).

Graphical Analysis

• A position-time graph shows an object's displacement vs. time, with the slope representing velocity.
• A velocity-time graph shows an object's velocity vs. time, with the slope representing acceleration.
• An acceleration-time graph shows an object's acceleration vs. time.
• The slope of a position-time graph gives the velocity, and the slope of a velocity-time graph gives the acceleration.

Learn about the concepts of displacement, distance, speed, and velocity in one-dimensional motion kinematics, including their definitions and differences.