Difference Between Speed and Velocity

The rate of change of position of an object with time in any direction is called its speed. speed has only magnitude and no direction, so it is a scalar quantity. Different types of speeds exist. The speedometer of an automobile indicates its instantaneous speed at any instant.

The rate of change of position of an object with time in a given direction is called its velocity. Velocity has both magnitude and direction, so it is a vector quantity. Different types of velocity exist.

In this article, we will discuss speed, and types of speed, velocity and types of velocity, which belong to the chapter kinematics, which is an important chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), more than fifteen questions have been asked on this concept. And for NEET three questions were asked from this concept.

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This Story also Contains

1. Define Speed and Velocity
2. Velocity
3. Relation between Speed and Velocity:
4. Solved Examples Based on Speed And Velocity
5. Conclusion

Define Speed and Velocity

Speed is the quantity which shows how fast the body is moving but velocity is the quantity which shows the speed as well as the direction of the moving body. "Velocity is speed with displacement," asserts the relationship between speed and velocity.

Formula:

Speed = Change in distance change in time v= distance time

Tips of Speed

1. S.I. unit →ms−1 or meters per second.

2. Dimensions =LT−1

3. Speed is a scalar quantity.

• E.g.: If a body covers a distance of 18m in 1 sec then the speed will be:

Using the formula of speed,

v= distance time =18 m1 s⇒18 m/s

After speed, now let's shift to the concept of average and instantaneous speed.

Average Speed and Instantaneous Speed

Average Speed: Amount of total distance covered in total time.

Mathematically average speed can written as,

Average speed = total distance covered total time taken ,vav=st

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

vav=st⇒50 m5 s=10 m/s Average Speed =10 m/s

Tips for Average Speed

If an object or body covers s1 distance in t1 time and s2 distance in t2 time then average speed is calculated by the formula:

Vav=s1+s2t1+t2

Instantaneous Speed

• It is the speed at that particular instant or small interval of time.

Mathematically,

vinst =limΔt→0ΔxΔt

Let's discuss the velocity and types of velocity in detail

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The magnitude of the rate of change of an object's position with time or the magnitude of change of its position per unit of time is the speed of an object in everyday use and kinematics. The distance travelled by an object in a given time interval is divided by the duration of the period; the instantaneous speed is the average speed's limit as the interval's duration approaches zero.

The metrics of speed are distance divided by time. The kilometre per hour is the most often used unit of speed in everyday life. According to special relativity, the fastest feasible speed at which energy or information may travel is the speed of light in a vacuum.

Galileo Galilei is credited with being the first to estimate speed by taking into account the distance travelled and the time it takes to complete the journey. Galileo defined speed as the amount of time it takes to travel a certain distance.

Instantaneous speed is the speed at a specific point in time, or the speed considered to be constant for a very brief period of time. A speedometer can be used to determine a car's instantaneous speed at any given time. The total distance travelled divided by the time period is the average speed over a finite time interval.

In contrast to instantaneous speed, average speed is calculated by dividing the total distance travelled by the time interval. The distance travelled per unit of time is known as linear speed, whereas the linear speed of something travelling in a circular route is known as tangential speed. In one complete rotation, a point on the outside edge of a merry-go-round or turntable travels a greater distance than a point closer to the centre.

Linear speed is larger on the outside edge of a rotating object than it is closer to the axis because you may go a longer distance in the same amount of time. The phrases linear speed and tangential speed are interchangeable in circular motion.

The number of revolutions per unit of time is known as rotational speed or angular speed. A rigid merry-go-round or turntable rotates in the same amount of time around its axis of rotation. As a result, all pieces rotate at the same rate, or turn the same number of times per unit of time. Rotational rates are commonly expressed in terms of revolutions per minute (RPM) or the number of "radians" spun in a unit of time.

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Velocity

Velocity is the rate of change of displacement. It is the displacement in unit time. It is a vector quantity. The unit of measurement of velocity is ms^-1.

velocity=displacement/Time taken

The velocity, which is a function of time, is the rate at which an object's position changes with respect to a frame of reference. A definition of an object's speed and direction of travel (e.g. 80 km/h to the south) is identical to velocity. Velocity is a key concept in kinematics, the part of classical mechanics that explains body motion.

Velocity is a fundamental vector quantity that must be defined in terms of both magnitude and direction. Speed is the scalar objective measurement of velocity, and it is a cohesive measure of distance whose quantity is measured in metres per second in the SI (metric measurements).

Velocity refers to the speed with which anything moves or acts. The measurement of the rate and direction of change in location of an item is known as velocity in physics. It is a vector quantity that indicates a body's speed as well as its motion direction.

The rate of change of location with respect to time is defined as velocity, which is also referred to as instantaneous velocity to underline the distinction from average velocity. The average velocity of an object is always less than or equal to its average speed.

This can be seen by recognizing that, whereas distance is always strictly rising, displacement can change direction as well as increase or decrease in magnitude.

The velocity aggregated across time is the same as the average velocity. The word "relative velocity" refers to the measurement of velocity between two objects in a single coordinate system. Many systems in physics deal with the relative motion of two or more particles, hence relative velocity is important in both classical and current physics.

Mathematically,

V= displacement time

Tips For Velocity

1. 1. S.I. unit →m/s

2. Dimensions- LT−1

3. Velocity is a vector quantity.

4. Velocity is also called speed in a definite (particular) direction.

After reading about velocity, now let's read the average and instantaneous velocity.

Average Velocity and Instantaneous Velocity

Average Velocity: Amount of total displacement covered in total time.

Mathematically,

Average Velocity = Total Displacement Total time taken ,V→avg =S→net t

Instantaneous Velocity: It is Velocity at that particular instant or small interval of time.

Mathematically,

V→inst =limΔt→0Δx→Δt

Relation between Speed and Velocity:

Similarities between speed and velocity:

• Both speed and velocity are ways of calculating an object's change in position over time.
• In practice, an object's speed and velocity are the same in a straight line motion. Since distance and displacement will be the same.
• Because they are both physical quantities, they can both be measured and quantified.
• The units of speed and velocity are the same, metres per second or m/s.

Difference between Displacement and Velocity:

• The vector difference between an object's ending and starting coordinates is known as displacement.
• The frequency at which displacement changes over time is referred to as velocity.

NCERT Physics Notes :

• NCERT Notes class 11 physics
• NCERT Notes class 12 physics
• NCERT Notes for all subject

Difference between Motion and Speed:

• A change in the location of an object over time is referred to as motion. Displacement, distance, velocity, acceleration, time, and speed are all terms used to describe motion.
• The ratio of distance to time (a scalar quantity) is the average speed. Speed is unconcerned about direction.

Difference between Speed and Distance:

• The term "distance" refers to the amount of space between two points.
• The pace at which a distance changes is referred to as speed.
• If D is the distance travelled by an item in time T, then s =DT is the speed. The units are the same as for velocity.

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Solved Examples Based on Speed And Velocity

Example 1: A body travels $100 \mathrm{~km}$ southwest and then $50 \sqrt{2} \mathrm{~km}$ in the northern direction. The total magnitude of the velocity if the time taken is $1 \mathrm{hr}$.

1) $100+50 \sqrt{2} \mathrm{~km} / \mathrm{hr}$
2) $100-50 \sqrt{2} \mathrm{~km} / \mathrm{hr}$
3) $50 \sqrt{2} \mathrm{~km} / \mathrm{hr}$
4) $100 \mathrm{~km} / \mathrm{hr}$

Solution:

As we learned,

$\text { Average Velocity }=\frac{\text { Total Displacement }}{\text { Total time taken }}$

So,

Displacement

$\begin{aligned}
& =O B=50 \sqrt{2} \mathrm{~km} \\
& \therefore \text { Average velocity }=\frac{50 \sqrt{2} \mathrm{~km}}{1 \mathrm{hr}}=50 \sqrt{2} \mathrm{~km} / \mathrm{hr}
\end{aligned}$

Example 2: An object moving with a speed of $6.25 \mathrm{~ms}^{-1}$, is decelerated at a rate given by $\frac{d v}{d t}=-2.5 \sqrt{v}$ where $v$ is the instantaneous speed. The time taken (in seconds) by the object, to come to rest, would be:

1) 2

2) 1

3) 4

4) 8

Solution:

$ \begin{aligned}
& \frac{d v}{d t}=-2.5 \sqrt{v} \text { or } \frac{1}{\sqrt{v}} d v=-2.5 d t \\
& \int_{v 1}^{v 2} \frac{d v}{\sqrt{v}}=-2.5 \int_0^t d t \\
& v_1=6.25 \mathrm{~ms}^{-1} \\
& v_2=0 \\
& 2\left[v^{1 / 2}\right]_{6.25}^0=-2.5 t \Rightarrow t=\frac{-2 \times(6.25)^{1 / 2}}{-2.5} \\
& t=2 \text { sec }
\end{aligned}$

Hence, the answer is option (1).

Example 3: A particle moves such that its position vector $\widehat{r}(t)=\cos \omega t \hat{i}+\sin \omega t \hat{j}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle :
1) $\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$
2) $\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away from the origin
3) $\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$
4) $\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards the origin

Solution:

$\begin{aligned}
& \vec{r}=\cos \omega t i+\sin \omega t j \\
& \vec{v}=\frac{d \vec{r}}{d t}=-\omega \sin \omega t i+\omega \cos \omega t j \\
& \vec{a}=\frac{d \vec{v}}{d t}=-\omega^2(\cos \omega t i+\sin \omega t j)=-\omega^2 \vec{r}
\end{aligned}$

implies a is anti-parallel to r

$\vec{v} \cdot \vec{r}=0$

Implies v is perpendicular to r

Hence, the answer is the option (4).

Example 4: A particle moves $50 \mathrm{~m}$ in 5 seconds, then $20 \mathrm{~m}$ in the next 4 seconds and $30 \mathrm{~m}$ in the next 7 seconds, then the average speed (in $\mathrm{m} / \mathrm{s}$ ) of the particle is :

1) 6.25

2) 7.25

3) 8.50

4) 5

Solution:

Tips for average speed. -

If an object or body covers s₁ distance in t₁ time and s₂ distance in t₂ time then average speed is calculated by the
formula

$V_{a v}=\frac{s_1+s_2}{t_1+t_2}$

Total distance travelled = (50 + 20 + 30 ) m = 100 m

Total time taken = 16 Seconds.

$\therefore \text { Average speed }=\frac{100}{16} \mathrm{~m} / \mathrm{sec}=6.25 \mathrm{~m} / \mathrm{sec}$

Hence, the answer is the option (1).

Example 5: A particle travelled first 10 m with 2 m/s, the next 10 m with 3 m/s and the last 10 m with 6m/s then its average speed is (in m/s) :

1) 3

2) 4

3) 5

4) 6

Solution:

Tips for average speed

If an object or body covers s₁ distance in t₁ time and s₂ distance in t₂ time then average speed is calculated by the
formula

$V_{a v}=\frac{s_1+s_2}{t_1+t_2}$

Total distance = ( 10 + 10 + 10 ) m = 30 m

$\text { Total time }=\frac{10}{2}+\frac{10}{3}+\frac{10}{6}=\frac{30+20+10}{6} \sec =10 \mathrm{sec}$

$\text { Average Speed }=\frac{\text { Total distance }}{\text { Total time }}=\frac{30 \mathrm{~m}}{10 \mathrm{sec}}=3 \mathrm{~m} / \mathrm{s}$

Hence, the answer is the option (1).

Conclusion

Speed is equal to the distance travelled by the object per unit of time whereas Velocity is equal to the displacement covered per unit time. Speed can be positive or zero but never negative whereas velocity can be positive, zero or negative depending on the displacement is positive, zero or negative.

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