When an object all of a sudden changes its velocity and /or direction, we can always find an interaction between that object and its surroundings that is responsible for this change. We say that the surroundings exert a force on the object. Under the influence of the force, the object will accelerate. By the law of forces together with the properties of the body and its environment, we can calculate the force acting on the object. The laws of motion are then used to calculate the acceleration of the object under influence of these forces.

The study of motion is called kinematics. The word kinematics comes from the Greek word kinema, meaning motion. Kinematics is the science of motion. Kinematics describes the positions and motions of objects in space as a function of time but does not consider the causes of motion. In human movement, it is the study of the positions, angles, velocities, and accelerations of body segments and joints during motion. Precisely, kinematics involves position, velocity and acceleration (and their rotational equivalents).

Mathematically, the exact characteristic of the motion of objects is expressed by the shape and the slope of the lines on a position versus time. While an object is in motion, the velocity of the object and the rate of change of velocity per unit time at each point in time are necessary. We will introduce three important concepts related to motion: position, velocity, and acceleration.

View a Video

Position

The first concept needed in depicting the motion of an object is its position relative to some fixed reference point. Position is the point in space that an object occupies, this needs to be defined in some coordinate system. This involves two issues: the distance the object is away from a reference point, and also the direction relative to that reference point. The position is therefore a vector quantity since it has both a magnitude (the distance) and a direction. Occasionally we wish to talk about the position of an object relative to its starting point at some initial time. This is called the displacement of the object. Displacement may also be defined as the straight line distance between the initial position x_i and final position x_f of the body. The net change in position (displacement) is given by

The symbol D is used to indicate a change in position x.

Mathematically, position is a function that can be either scalar-valued x(t) (for motion in one dimension) or vector-valued x(t) (for motion in two or three dimensions). At each point in time its value represents the position of an object at a particular time.

Velocity

For an object in motion the function of velocity is important. This function is the time derivative of the position function and gives the velocity of an object at each point in time. Note that, as with the position, the velocity is a vector: it has a magnitude and a direction associated with it.

Sometimes only the magnitude of the velocity is of interest. It is then called the speed, which is the most basic property of a moving body. The speed is the ratio of the distance traveled to the time required from the travel. The average speed is defined as the total distance, s, traveled during a particular time divided by that time interval, t

If the average speed is the same for all parts of a trip, then the speed is constant.

Example: Velocity-time graph

Acceleration

Acceleration a(t) is a very important concept in Newtonian physics. Just as the velocity involves a rate of change of position in time, the acceleration of an object describes the rate of change of velocity per unit time, and is hence usually given in units such as m/s². Therefore, an object whose velocity is changing is said to be accelerating. Following a similar approach as before, we define the average acceleration a_ave, as the change in velocity divided by the time required for the change. It may be defined as

 or in symbol 

where v₂ is the final velocity and v₁ is the initial velocity. Simple algebra gives

View a Video

Example: Deceleration

Coordinate Systems

To precisely describe motion, we must be able to say where an object is located within a given reference frame. For example we can locate a chair in a room by saying it is 2 m away from the door, 3 m away from the window, and 0.5 m away from a table. When we say space is three dimensional, we mean we need three numbers to completely locate the position of an object or point. A system for assigning these three numbers, or coordinates, to the location of a point in a reference frame is called a coordinate system. Most frequently, we will use a Cartesian (rectangular) system that describes the position in terms of x, y, z coordinates. However, you are free to choose the coordinate system you wish to use, orient it the way you want, and place its origin wherever you prefer.