Physics 1005 Week 2

Velocity and Acceleration

• Velocity: Velocity is the distance an object moves over time. In the context of this study, velocity is treated as synonymous with speed and can be mathematically represented as:[ V = \frac{\text{distance traveled}}{\text{time traveled}} ]

• Acceleration: Acceleration refers to the rate of change of velocity of an object. It indicates how quickly an object is speeding up or slowing down.

  • If an object's speed is changing, it is said to be accelerating. If its speed remains constant, it is not accelerating, hence acceleration is zero.

  • The formula for acceleration is defined as:[ a = \frac{U_f - V_i}{t} ]Where:

  • ( a ) = acceleration

  • ( U_f ) = final velocity of the object

  • ( V_i ) = initial velocity of the object

  • ( t ) = time duration over which the change occurs

• Inertia: Inertia is the property of an object to resist changes in its state of motion. It is directly related to mass; more massive objects have greater inertia and are more resistant to changes in motion.

  • For example, a train is more massive than a bicycle, making it harder to stop when in motion and harder to set in motion when at rest. The greater the mass of an object, the greater its inertia.

• Newton's Second Law: The second law provides a fundamental equation in physics:[ \sum F = m \cdot a ]Where:

  • ( \sum F ) = total (net) force acting on the object

  • ( m ) = mass of the object (which relates to its inertia)

  • ( a ) = acceleration of the object

This law describes how the total force acting on an object is equal to the product of its mass and its acceleration. Changes in either the force applied to an object or the object's mass can result in varying levels of acceleration.

• Zero Force: An object may experience zero net force acting on it in two situations:

  1. Multiple forces acting in opposite directions may cancel each other out, resulting in no net force.

  2. There may be no forces acting on the object at all.

  • It's essential to understand that even if the net force is zero, the object can still be moving. However, if the net force is zero, the object's speed must remain constant, indicating zero acceleration.

• Newton's First Law: This law states:"An object in motion will remain in motion at a constant velocity, and an object at rest will remain at rest unless acted upon by an unbalanced force." This concept helps to illustrate that a force is necessary to change the velocity of an object.

Work and Energy

• Work: In physics, work is defined as the force applied to an object multiplied by the distance over which that force is exerted in the direction of the force. This can be formalized as:[ W = F \cdot d ]Where:

  • ( W ) is work

  • ( F ) is force in Newtons (N)

  • ( d ) is distance in meters (m)

  • The unit of work (Joules) expresses how much energy is transferred when work is done:( 1 N \cdot m = 1 J )

• Energy: This general term refers to the ability to perform work. An object has energy if it can apply a force to move another object a certain distance. For example, a ball held above the ground has potential energy, which can be transformed into kinetic energy when it is dropped, applying force over the distance it falls:

  1. Kinetic Energy (KE): This form of energy relates to the motion of an object. The faster an object moves, the greater its kinetic energy.

  2. Potential Energy (PE): This form of energy is associated with the position of an object, particularly in relation to a gravitational field or due to its position in a spring. For instance, a ball elevated above the ground holds gravitational potential energy.

• Conservation of Energy: One of the fundamental principles in physics is the conservation of energy, which states: Energy cannot be created or destroyed; it can only change forms or be transferred. The total energy in an isolated system remains constant, even though it may be transformed from one type to another (e.g., potential energy to kinetic energy).