Question

Which of the following is one dimensional motion?
(A) Landing of aircraft
(B) Earth revolving around the sun
(C) Motion of the wheels of moving train
(D) Train running on a straight track

Answer 1

One dimensional motion is motion along a straight line. The line used for this motion is often the familiar x-axis. The object may move forward or backward along this line: Forward is usually considered positive movement, and this movement is usually considered to be to the right.

Complete step by step solution:
One dimensional motion also called 1D motion is a straight line motion. When a particle is constrained to move on a straight line, the description becomes fairly simple. We choose the line as the X-axis and a suitable time instant as $t = 0.$
Generally the origin is taken at the point where the particle is situated at $t = 0.$ the position of the particle at time $t$ is given by its coordinate $x$ at that time. The velocity is
$v = \dfrac{{dx}}{{dt}}$
And the acceleration is

a& = &{\dfrac{{dv}}{{dt}}} \\\ {}& = &{\dfrac{d}{{dt}}\left( {\dfrac{{dx}}{{dt}}} \right)} \\\ {}& = &{\dfrac{{{d^2}x}}{{d{t^2}}}} \end{array}$$ If $\dfrac{{dx}}{{dt}}$ is positive, the direction of the velocity is along the positive X-axis and if $\dfrac{{dx}}{{dt}}$ is negative, the acceleration is along the negative X-axis. Similarly if $$\dfrac{{dv}}{{dt}}$$ is positive, the acceleration is along the positive X-axis and if $$\dfrac{{dv}}{{dt}}$$ is negative, the acceleration is along the negative X-axis. Now among the given situations i.e. landing of aircraft, earth revolving around the sun, motion of wheels of moving train and train running on straight track the last one follows the condition of one dimensional motion rest other are either two dimensional or three dimensional motion. **Note:** The straight line motion, also called the Rectilinear Motion can be of two types: 1\. Uniform linear motion with constant velocity or zero acceleration 2\. Non-Uniform linear motion with variable velocity or non-zero acceleration Linear motion is the simplest kind of one-dimensional motion. As Newton’s law of motion suggests, an object will either be at rest or continue to move in a straight line with a uniform velocity unless and until an external force is applied to it.