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Speed and velocity - (Concept)

I.   Speed

  • Rate of change of distance with time.

  • Formula-

$
\begin{aligned}
\text { Speed } & =\frac{\text { Change in distance }}{\text { change in time }} \\
v & =\frac{\text { distance }}{\text { time }}
\end{aligned}
$

- Tips of Speed-
1. S.I. unit $\rightarrow \mathrm{ms}^{-1}$ or meters per second.
2. Dimensions $=L T^{-1}$
3. Speed is a scalar quantity.
- E.g: A body covers a distance of 18 m in 1 sec

Using the formula of speed.

$
v=\frac{\text { distance }}{\text { time }}=\frac{18 \mathrm{~m}}{1 \mathrm{~s}} \Rightarrow 18 \mathrm{~m} / \mathrm{s}
$


II . Average Speed and Instantaneous Speed
1. Average Speed-
- Amount of total distance covered in total time.
- Formula-

$
\text { Average speed }=\frac{\text { total distance covered }}{\text { total time taken }} v_{a v}=\frac{s}{t}
$

- E.g A body covers a total distance of 50 m with variable speed in 5 sec .

$
v_{a v}=\frac{s}{t}
$
 

      

$
\Rightarrow \frac{50 \mathrm{~m}}{5 \mathrm{~s}}=10 \mathrm{~m} / \mathrm{s}
$


$
\text { Average Speed }=10 \mathrm{~m} / \mathrm{s}
$

- Tips for average speed-

If an object or body covers s1 distance in t 1 time and s 2 distance in t 2 time then average speed is calculated by the Formula- $V_{a v}=\frac{s_1+s_2}{t_1+t_2}$
2. Instantaneous Speed-
- It is the speed at that particular instant or small interval of time.
- Formula-

$
v_{\text {inst }}=\lim _{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t}
$

III. Velocity
- Rate of change of displacement with time.
- Formula-

$
V=\frac{\text { displacement }}{\text { time }}
$
 

  • Tips For velocity-

  1. S.I. unit \rightarrow  m/s

  2.  Dimensions- $L T^{-1}$
    3. Nelocity is a vector quantity.
    4. Velocity is also called speed in a definite (particular) direction.
    IV. Average Velocity and Instantaneous Velocity
    1. Average Velocity-
    - Amount of total displacement covered in total time.
    - Formula-

    Average Velocity $=\frac{\text { Total Displacement }}{\text { Total time taken }}, \vec{V}_{\text {avg }}=\frac{\vec{S}_{\text {net }}}{t}$
    2. Instantaneous Velocity-
    - It is Velocity at that particular instant or small interval of time.
    - Formula-

    $
    \vec{V}_{\text {inst }}=\lim _{\Delta t \rightarrow 0} \frac{\overrightarrow{\Delta x}}{\Delta t}
    $

V.     Uniform motion and Non-uniform motion

  1. Uniform motion-

  • If equal distance/displacement is covered in equal intervals of time, how small these intervals may be.

  • Uniform speed-If equal distances are covered in equal intervals of time.

  • Uniform velocity-If equal displacement are covered in equal intervals of time.

  • Uniform speed and Uniform velocity is the same as uniform motion.

  • For uniform motion along a straight line, the average and instantaneous velocities have the same values.

  1. Non-uniform motion- 

  •  If equal distance/displacement is covered in unequal intervals of time.

  • Non-uniform speed-If equal distances are covered in unequal intervals of time.

  • Non-uniform velocity-If equal displacement are covered in unequal intervals of time.

  • Non-uniform speed and Non-uniform velocity  is same as Non uniform motion

Exam Chapter
JEE MAIN Kinematics
Physics Part I Textbook for Class XI
Page No. : 42
Line : 60

Average speed is defined as the total path length travelled divided by the total time interval during which the motion has taken place :
Average\;speed = \frac{Total\;path\; length }{Total\;time\;interval} = \frac{Change\, in \, distance}{change \, in\, time}


Concepts of Physics Part-1
Page No. : 32
Line : 53

Understanding Physics (Volume-1)
Page No. : 131
Line : 9

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