# Question 0ff30

Jul 29, 2015

When a body is moving along a straight line, it's motion is termed as rectilinear motion. Given below are some basic features and results of rectilinear motion which do of course hold for other types of motions as well.

#### Explanation:

1) The distance traveled by an object is called the path length. The path length is a scalar and is a positive number. It says nothing about the position of the object from the origin.

2) The change in position of an object along the straight line path i.e. the difference between the initial and final positions is called the displacement. It specifies how far the object has traveled from it's initial point. It can be positive as well as negative depending on the initial and final positions on the measuring axis (generally the x -axis).

3) Velocity, v is the rate of change of displacement with time. It is a vector but, in case of 1D motion, it can be treated as a scalar and as such it has both positive and negative values.

It is given as, $v = \frac{\mathrm{dx}}{\mathrm{dt}}$ where $x$ is the x - coordinate of the object.

4) Average velocity is the change in position/ the time taken. When the time taken approaches zero, we take the limit and then the average velocity becomes the instantenous velocity or simply velocity.

5) Accelaration is the time rate of change of velocity. It is written mathematically as,

$a = \frac{\mathrm{dv}}{\mathrm{dt}} = \frac{{d}^{2} x}{\mathrm{dt}} ^ 2$

6) The average acceleration is the change in velocity/ the time taken. When time period approaches zero, we take the limit of the expression and the average acceleration becomes the instantenous acceleration or simply acceleration.

7) The units of velocity is $m {s}^{-} 1$ and that of acceleration is $m {s}^{-} 2$ .

8) When the displacement is plotted with time, we get a displacement-time graph. The slope of the graph at any point gives the value of velocity at that point.

9) When velocity is potted against time, we get a velocity-time graph and the slope of the curve at any time gives the value of acceleration at that point.

10) For constant acceleration, we can derive some simply relationships between $a , v , x$ and $t$. They are called kinematic equations for uniformly accelerated motion and are given below.

$x = x {\text{_0 + v}}_{0} t + \frac{1}{2} a {t}^{2}$

2a(x - x""_0) = v^2 - v""_0^2

v = v""_0 + at#