 # Difference Between Speed And Velocity  View Notes

## Speed & Velocity

We often find the terms speed and the velocity as similar; however, practically, there’s a difference between them in them in terms of nature.

Let’s suppose I traveled 120 km in 5 hr, so obviously my speed will be distance/time, i.e., 120/5 or 24 kmph. So this was the case for the speed, now if I ask which directions I took in my journey and from starting, in the middle or while making turns and till the end, was my speed the same?  The answer will be clearly No; it’s because initially the speed was 0 when my car was at rest, when I started, it was slow, I also increased my speed, also decreased during the turns; on the whole, my speed wasn’t the same, which means I traveled with a velocity (varying speed) to cover 120 km distance in 5 hrs. Now. let’s discuss the difference between speed and velocity in tabular form:

 Speed Velocity Speed is simply the rate of change of motion. Velocity is direction-aware and it is the rate of change of position of an object. Speed is the distance traveled by a body in a  unit time. Velocity is the displacement covered by a body in a unit time. Speed is a scalar quantity Velocity is a vector quantity. Speed ascertains how fast a body moves. Velocity ascertains the object’s speed and the direction it takes while moving.

Speed: According to Galileo, speed is defined as the distance covered per unit time. For example, a man moving by car will cover a large distance as compared to a man moving by bicycle in the same time period. This is because a car can travel with more speed as compared to the bicycle. Speed is the magnitude part of the velocity in kinematics, thus it is a scalar quantity.

Its SI unit is meter per second. m/ s

Speed = $\frac{ distance}{time}$

Instantaneous Speed: Instantaneous speed is the speed at any instant. For example, instantaneous speed can be seen on the speedometer of any vehicle. In mathematical terms, it is defined as the magnitude of the instantaneous velocity that is the derivative of the position concerning time.

V=|v|=|$\frac{dr}{dt}$|

Average Speed: It is different from the instantaneous speed; average speed is the total distance travelled in a particular interval of time. In other words, the total covered distance divided by the total time interval is the average speed of the body.

Rotational Speed: It is rotating speed. In other words, the rotational speed is the number of turns made by a body in unit time.

Tangential Speed: It is defined as the linear speed of a body travelling along a circular path. Mathematically,

Tangential Speed= rotational speed x radial distance

v=rω

Thus, tangential speed will be directly proportional to r when all parts of a system

simultaneously have the same, as for a wheel, disk, or rigid wand.

Relative Speed: It is clear from its name that the speed of any body is relative to any other body that the speed a body can be seen with reference to another body.

There are Two Types of Speed:

1. Uniform Speed: When the distance travelled by a body is equal in equal interval of time then the speed is uniform.

2. Non-uniform Speed: When the distance travelled by a body is unequal in an equal interval of time then the speed is known as non- uniform speed.

3. Velocity: Velocity is a physical vector quantity. It has a magnitude as well as direction. In calculus, velocity is the first derivative of the position with respect to time. Velocity, in other words, is the rate of change in the position of the body with reference to time. Its SI unit is meter per second.

Velocity = $\frac{Displacement}{Time}$ = $\frac{Final Position−Initial Position}{Time}$

Initial and Final Velocity: Initial velocity describes the speed of an object when the force was applied initially on the body. The final velocity is the measurement of speed and direction of a dynamic body when it reaches its maximum acceleration.

Relative Velocity: It is fundamental in both classical and physical physics. Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system.

Types of Velocity:

1. Constant Velocity: A velocity which does not change with the direction and speed and moves along a straight line is called as constant velocity.

2. Changing Velocity: A velocity which changes with the speed and direction or changes either speed or direction is called changing velocity. This is also called as acceleration.

3. Instant (Instantaneous) Velocity: When at a particular time, speed and direction changes, then that phenomenon is called instantaneous velocity.

4. Terminal Velocity: When the gravity takes over an object and results in falling down of the object towards the earth through the atmosphere the phenomenon is called terminal velocity.

Distinguish Between Speed and Velocity

1. Speed is the distance covered in unit time whereas velocity is the displacement covered in unit time.

2. (Difference between distance and displacement- Distance, which is a scalar quantity deal with the total area covered by an object, whereas, a displacement which is a vector quantity deals with the change in the position of the object. The distance can never be zero, whereas, displacement can become zero)

3. Speed is a scalar quantity and velocity is a vector.

4. Speed only determines the magnitude that is how fast is a body moving whereas velocity determines the direction also that is in which direction the body is moving.

5. Speed is the rate of change of distance whereas velocity is the rate of change of displacement.

6. Speed can never be zero but the velocity can be positive, negative or zero. This is the difference between speed and velocity.

7. An object can possess the same speed and different velocities. Speed may or may not be equal to the velocity.

8. Speed and velocity both are measured in m/s

Test Yourself

1. A car travelled a total distance of 450 miles. The trip took 8 hours. What is the average speed?

2. Distance covered by the bicycle is 100km in 130sec. Find the speed of the bicycle.

3. A car travelled 24km in 2 hours. What was the average speed of the car?

4. A man walks takes 2 hours to walk 1 mile. What is the average speed of the man?

5. While on vacation, Aman drives a total distance of 536 m. The time taken to cover the distance was 7 hours. What was the average speed?

6. F1 Car travels 44km in only 24 minutes. Tell the average speed of F1.

7. A Bus took 8 hours to complete the journey from Ahmadabad to Warangal

8. which is 500km. Calculate the average speed of the bus.

9. Truck completed a distance of 300 miles and took 5 hours. Find the average speed in km per hour?

10. In a boat race of 1000 m, a boat takes 30 minutes. What is the velocity of the boat?

11. A ship is in a 1000 m race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 30 minute and 20 seconds. What is the velocity of the sailboat?

12. A snail can crawl 10 cm race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 20 minutes. What is the speed of the snail?

13. A sailor can sail his boat in a 100 m race, in its full speed the boat crosses the starting line and reaches the finish line in exactly 1 hour and 20 seconds. Find the velocity of the sail boat?

14. In a boat race of 100 m, a boat takes 120 seconds. What is the velocity of the boat?

15. A ship in its full speed crosses an 1111 m race line in exactly 33 minute and 22 seconds. What is the velocity of the sailboat?

16. A man drove his car for car for 45 miles. He stated driving at 12:00PM and reached at his destination at 05:00PM. What is his average speed?

17. Distance covered by the bicycle is 10km in 130sec. Find the speed of the bicycle.

18. Car travelled from Kanpur to Bareilly which is 520km far from each other. The car took 12 hours. What was the average speed?

19. A man walks 2 miles. He took 2 hours and 50 minutes. What was the average speed?

20. While on vacation, Amarendra drive a total distance of 530 m. His trip took 420 minutes. What was the average speed?

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