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Speed and velocity is considered one of the most asked concept.
32 Questions around this concept.
A body travels 100 km southwest and then $50 \sqrt{2} \mathrm{~km}$ in the northern direction. The total magnitude of the velocity if the time taken is 1 hr .|
A body moves along a semi-circle of radius (r) 1 m from point A to B in 3 seconds then its speed is
A particle is moving along a circular path with a constant speed of 10ms-1 . What is the magnitude of change in velocity of the particle, when it moves through an angle of 600 around the centre of the circle?
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A body moving along a straight line travels one-third of the total distance with a speed of . The remaining distance is covered with a speed of for the half time and for the other half-time. The average speed during the motion is :
The distance travelled by a particle is related to time as The velocity of the particle is :
The distance travelled by an object in time t is given by. The instantaneous speed of the object at t =5 s will be :
The position of a particle related to time is given by . The magnitude of the velocity of the particle at t = 2s will be :
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-
S.I. unit m/s
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
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.
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
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