Linear motion, also called rectilinear motion,[1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position , which varies with (time). An example of linear motion is an athlete running a 100-meter dash along a straight track.[2]
Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as gravity and friction can cause an object to change the direction of its motion, so that its motion cannot be described as linear.[3]
One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction. The analysis of such systems may therefore be simplified by neglecting the direction components of the vectors involved and dealing only with the magnitude.[2]
Velocity
Velocity refers to a displacement in one direction with respect to an interval of time. It is defined as the rate of change of displacement over change in time.[7] Velocity is a vector quantity, representing a direction and a magnitude of movement. The magnitude of a velocity is called speed. The SI unit of speed is that is metre per second.[6]
Instantaneous velocity
In contrast to an average velocity, referring to the overall motion in a finite time interval, the instantaneous velocity of an object describes the state of motion at a specific point in time. It is defined by letting the length of the time interval tend to zero, that is, the velocity is the time derivative of the displacement as a function of time.
The magnitude of the instantaneous velocity is called the instantaneous speed.The instantaneous velocity equation comes from finding the limit as t approaches 0 of the average velocity. The instantaneous velocity shows the position function with respect to time. From the instantaneous velocity the instantaneous speed can be derived by getting the magnitude of the instantaneous velocity.
Jerk
The rate of change of acceleration, the third derivative of displacement is known as jerk.[11] The SI unit of jerk is . In the UK jerk is also referred to as jolt.
Jounce
The rate of change of jerk, the fourth derivative of displacement is known as jounce.[11] The SI unit of jounce is which can be pronounced as metres per quartic second.
In case of constant acceleration, the four physical quantities acceleration, velocity, time and displacement can be related by using the equations of motion[12][13][14]
V→f=V→i+a→t
d→=V→it+½a→t²
V→²f=V→²i+2a→*d→
d→=½(V→f+V→i)t
here,
- is the initial velocity
- is the final velocity
- is the acceleration
- is the displacement
- is the time
These relationships can be demonstrated graphically. The gradient of a line on a displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under a graph of acceleration versus time is equal to the change in velocity.
Resnick, Robert and Halliday, David (1966), Physics, Section 3-4
- Resnick, Robert and Halliday, David (1966), Physics, Chapter 3 (Vol I and II, Combined edition), Wiley International Edition, Library of Congress Catalog Card No. 66-11527
- Tipler P.A., Mosca G., "Physics for Scientists and Engineers", Chapter 2 (5th edition), W. H. Freeman and company: New York and Basing stoke, 2003.