Uniform Acceleration and Graphical Representation

Study Notes

Uniform acceleration occurs when an object's velocity changes at a constant rate.
The acceleration of an object is uniform if it travels equal distances in equal times.
The acceleration is constant, meaning it does not change with time.

Distance-Time Graphs:
- A straight line indicates uniform motion.
- A curved line indicates non-uniform motion.
- The slope of the line represents the velocity.
Velocity-Time Graphs:
- A straight line indicates uniform acceleration.
- A curved line indicates non-uniform acceleration.
- The slope of the line represents the acceleration.
- The area under the curve represents the displacement.

First Equation of Motion:
- v = u + at
- where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Second Equation of Motion:
- s = ut + (1/2)at^2
- where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
Third Equation of Motion:
- v^2 = u^2 + 2as
- where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

Relative Motion: The motion of an object relative to another object or a frame of reference.
Types of Relative Motion:
- Translational Motion: When two objects move in the same direction.
- Rotational Motion: When two objects move in a circular path.
Relative Velocity: The velocity of one object relative to another object or a frame of reference.
Relative Acceleration: The acceleration of one object relative to another object or a frame of reference.

Uniform acceleration occurs when an object's velocity changes at a constant rate.
The acceleration of an object is uniform if it travels equal distances in equal times.
The acceleration is constant, meaning it does not change with time.

Distance-time graphs show uniform motion with a straight line and non-uniform motion with a curved line.
The slope of the distance-time graph represents the velocity.
Velocity-time graphs show uniform acceleration with a straight line and non-uniform acceleration with a curved line.
The slope of the velocity-time graph represents the acceleration.
The area under the velocity-time graph represents the displacement.

The first equation of motion is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
The second equation of motion is s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
The third equation of motion is v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

Relative motion is the motion of an object relative to another object or a frame of reference.
Translational motion occurs when two objects move in the same direction.
Rotational motion occurs when two objects move in a circular path.
Relative velocity is the velocity of one object relative to another object or a frame of reference.
Relative acceleration is the acceleration of one object relative to another object or a frame of reference.