One Dimensional Kinematics

Vectors:

The majority of units for the following are vectors. A vector is a mathematical object that has both magnitude and direction. It is often represented by an arrow pointing in a certain direction, with the length of the arrow representing the magnitude of the vector. Vectors can be added and subtracted using a process called vector addition.

To add two vectors, we draw them both starting from the same point and then draw the resultant vector from the starting point to the end point of the two vectors. The resultant vector is the vector sum of the two original vectors.

To find the vector sum C, we draw C starting from the starting point of A and B and ending at the end point of B. The vector sum C is then equal to the displacement from the starting point to the end point, which is (4,2) in this case.

Vector subtraction works in a similar way. To find the difference between two vectors A and B, we draw B starting from the end point of A and then draw the resultant vector from the starting point of A to the starting point of B. The resultant vector is the vector difference between A and B.

It is important to understand vectors to understand physics!

Formulas & Definitions:

• Distance: Distance is a scalar quantity that represents the length of a path between two points. It is a measure of how much ground an object has covered and is usually expressed in units of length such as meters or feet. It is calculated using the following formula:
  • Distance = Distance traveled
• Displacement: Displacement is a vector quantity that represents the change in position of an object. It is the shortest distance between the initial and final position of an object and is usually expressed in units of length such as meters or feet. It is calculated using the following formula:
  • Displacement = Final position - Initial position
• Speed: Speed is a scalar quantity that represents the rate at which an object moves. It is defined as the distance traveled divided by the time taken to travel that distance and is usually expressed in units of length per time such as meters per second or miles per hour. It is calculated using the following formula:
  • Speed = Distance traveled / Time taken
• Velocity: Velocity is a vector quantity that represents the speed of an object in a specific direction. It is defined as the displacement of an object divided by the time taken to travel that displacement and is usually expressed in units of length per time such as meters per second or miles per hour. It is calculated using the following formula:
  • Velocity = Displacement / Time taken
• Acceleration: Acceleration is a vector quantity that represents the rate at which an object's velocity changes. It is defined as the change in velocity divided by the time taken for that change and is usually expressed in units of length per time squared such as meters per second squared or feet per second squared. It is calculated using the following formula:
  • Acceleration = Change in velocity / Time taken for the change

Projectile Motion:

• Initial velocity: The initial velocity of a projectile is the velocity with which it is launched. It is a vector quantity that has both magnitude and direction. The initial velocity of a projectile can be broken down into two components: the horizontal component (vx) and the vertical component (vy). These components can be calculated using the following formulas:
  • vx = v0cos(theta) vy = v0sin(theta)
  • where v0 is the magnitude of the initial velocity and theta is the angle of launch measured from the horizontal.
• Time of flight: The time of flight of a projectile is the total time that it is in the air. It can be calculated using the following formula:
  • t = (2*vy)/g
  • where vy is the vertical component of the initial velocity and g is the acceleration due to gravity (9.81 m/s^2).
• Maximum height: The maximum height of a projectile is the highest point that it reaches during its flight. It can be calculated using the following formula:
  • hmax = (vy^2)/(2*g)
  • where vy is the vertical component of the initial velocity and g is the acceleration due to gravity (9.81 m/s^2).
• Range: The range of a projectile is the horizontal distance covered by the projectile. It can be calculated using the following formula:
  • R = (vx^2)/g
  • where vx is the horizontal component of the initial velocity and g is the acceleration due to gravity (9.81 m/s^2).

One-Dimensional Motion:

The kinematic equations for one-dimensional motion with constant acceleration are:

Vocabulary:

• One-dimensional motion: One-dimensional motion refers to motion in a straight line. This means that an object's position can be described by a single coordinate such as its distance from a fixed point.
• Average speed: Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of how fast an object is moving over a certain period of time.
• Instantaneous speed: Instantaneous speed is the speed of an object at a particular instant in time. It is the limit of the average speed as the time interval gets smaller and smaller.
• Vector quantities: Vector quantities have both magnitude and direction. Examples include displacement, velocity, and acceleration.
• Scalar quantities: Scalar quantities have only magnitude. Examples include distance and speed.
• Two-dimensional motion: Two-dimensional motion refers to motion that occurs in two dimensions, such as on a plane. This means that an object's position can be described by two coordinates, such as its distance from two fixed points.
• Projectile motion: Projectile motion refers to the motion of an object that is launched into the air and is subject to the force of gravity. The path of a projectile is a parabolic curve.
• Initial conditions: Initial conditions refer to the starting conditions of an object at a particular time, such as its position, velocity, and acceleration.
• Range: Range is the horizontal distance covered by a projectile. It is the horizontal component of the displacement of the projectile.
• Time in the air: Time in the air is the total time that a projectile is in the air. It can be calculated using the kinematic equation for time.