Rectilinear motion: Linear motion (also called rectilinear motion) is a 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 or zero acceleration and non uniform linear motion with variable velocity or non-zero acceleration. This type of motion describes the movement of a particle or a body. A body is said to experience rectilinear motion if any two particles of the body travel the same distance a
Rectilinear
motion: Linear motion
(also called rectilinear motion)
is a 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 or zero acceleration and non uniform linear motion
with variable velocity or non-zero acceleration. This type of motion
describes the movement of a particle or a body. A body is said to
experience rectilinear motion if any two particles of the body travel
the same distance along two parallel straight lines. The figures
below illustrate rectilinear motion for a particle and body. Fig. 1
shows (a) Rectilinear motion of a particle; (b) Rectilinear motion of
a body.
(a) (b)
Fig 1
In the above figures, x(t) represents the position of the particles along the direction of motion, as a function of time t. Given the position of the particles, x(t), we can calculate the displacement, velocity, and acceleration.
The acceleration is given by
where a is the acceleration, which we define as constant.
Integrate the above equation with respect to time, to obtain velocity. This gives us
where v(t) is the velocity and C1 is a constant.
Integrate the above equation with respect to time, to obtain position. This gives us