Speed And Velocity - Practice Questions & MCQ

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   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.

2. 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