# 2.6 One dimensional motion with constant acceleration  (Page 5/6)

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## Interpretation of equations of motion

One dimensional motion felicitates simplified paradigm for interpreting equations of motion. Description of motion in one dimension involves mostly the issue of “magnitude” and only one aspect of direction. The only possible issue of direction here is that the body undergoing motion in one dimension may reverse its direction during the course of motion. This means that the body may either keep moving in the direction of initial velocity or may start moving in the opposite direction of the initial velocity at certain point of time during the motion. This depends on the relative direction of initial velocity and acceleration. Thus, there are two paradigms :

• Constant force is applied in the direction of initial velocity.
• Constant force is applied in the opposite direction of initial velocity.

Irrespective of the above possibilities, one fundamental attribute of motion in one dimension is that all parameters defining motion i.e initial velocity, final velocity and acceleration act along a straight line.

## Constant acceleration (force) is applied in the direction of velocity

The magnitude of velocity increases by the magnitude of acceleration at the end of every second (unit time interval). In this case, final velocity at any time instant is greater than velocity at an earlier instant. The motion is not only in one dimension i.e. linear , but also unidirectional. Take the example of a ball released (initial velocity is zero) at a certain height ‘h’ from the surface. The velocity of the ball increases by the magnitude of ‘g’ at the end of every second. If the body has traveled for 3 seconds, then the velocity after 3 seconds is 3g (v= 0 + 3 x g = 3g m/s).

In this case, all parameters defining motion i.e initial velocity, final velocity and acceleration not only act along a straight line, but also in the same direction. As a consequence, displacement is always increasing during the motion like distance. This fact results in one of the interesting aspect of the motion that magnitude of displacement is equal to distance. For this reason, average speed is also equal to the magnitude of average velocity.

$\begin{array}{l}s=|x|\end{array}$

and

$\begin{array}{l}\frac{\Delta s}{\Delta t}=|\frac{\Delta x}{\Delta t}|\end{array}$

## Constant acceleration (force) is applied in the opposite direction of velocity

The magnitude of velocity decreases by the magnitude of acceleration at the end of every second (unit time interval). In this case, final velocity at any time instant is either less than velocity at an earlier instant or has reversed its direction. The motion is in one dimension i.e. linear, but may be unidirectional or bidirectional. Take the example of a ball thrown (initial velocity is ,say, 30 m/s) vertically from the surface. The velocity of the ball decreases by the magnitude of ‘g’ at the end of every second. If the body has traveled for 3 seconds, then the velocity after 3 seconds is 30 - 3g = 0 (assume g = 10 $\phantom{\rule{2pt}{0ex}}m/{s}^{2}$ ).

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