We commonly confuse the terms speed and velocity; yet, there is a practical distinction between them in nature.
Let’s say a person walks 4 km in 1 hour; his speed will be distance/time or 4/1 or 4 kmph. This was the case with speed. Now, is we ask which routes he travelled in his journey, and from starting, in the middle or when making turns and till the end, his pace remained the same, i.e. 4kmph? The answer is plain No.
This is because initially, at the start of his journey, his speed was 0, his speed decreased at an uphill slope. He stopped mid away due to some obstacles in his way. On the whole, his speed wasn’t consistent throughout the journey, which means he travelled at a velocity (changing speed) to cover 4 kilometres in an hour.
Let’s look at what is speed and velocity, along with the differences between them, in the following table.
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Speed |
Velocity |
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Speed is simply the magnitude of the rate of change of position with time. |
Velocity is the rate of change of position of a body, and it is a direction-dependent quantity. |
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Speed is the distance travelled by a body in a unit of time. |
Velocity is the displacement covered by an object in unit time. |
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Speed is a scalar quantity |
Velocity is a vector quantity. |
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Speed implies how fast a body moves. |
Velocity represents the object’s speed and also the directions it follows throughout its journey. |
What is speed?
Speed: According to the standard definition, speed is simply the distance travelled by the body in unit time. That means the greater the speed of an object, the larger the distance it will cover in a given time.
Speed= Distance/Time
Instantaneous speed: It is the speed of an object at any given moment. For example, the instantaneous speed of a moving vehicle can be observed on the speedometer. It is defined mathematically as the magnitude of instantaneous velocity.
Average speed: Unlike instantaneous speed, average speed refers to the entire distance travelled in a given period. In other terms, the average speed of the body is the total distance traversed divided by the total period.
Average speed=Total distance/Total time
Relative speed: It is the speed of any moving object concerning any other object or frame of reference. The frame of reference. (From where the motion of the object is being studied) can either be stationary or moving.
Rotational speed: It is generally defined for objects that are either rotating or revolving around any axis of rotation. Mathematically it is the total number of turns/rotation a body makes in a given amount of time, specified by revolutions per minute(rpm).
Tangential speed: It is defined as the linear speed of a body travelling in a circular path. It is always perpendicular to the line joining the axis/centre of rotation and the moving object.
Mathematically its value can be found by-
Tangential speed= radial distance*angular speed
v=r*ω
It is important to note that if the angular speed is kept constant for a body. Tangential speed will be directly proportional to the radius/distance of the body from the centre/axis of rotation, i.e. Tangential speed of any object will increase as we move away from the centre/axis of rotation if the angular speed is kept constant.
There are 2 types of speed:
- Uniform speed: When a moving object covers equal distance in equal intervals of time, its speed is said to be uniform.
- Non-uniform speed: when a body travels the unequal distance in equal intervals of time, its speed is non-uniform.
Velocity- Velocity is defined as the rate of change of displacement. It is a vector quantity, i.e. it has both magnitudes as well as direction. Its S.I. unit is a meter per second.
Velocity= Total displacement/Total time
Relative velocity: Velocity of a moving body for another body/frame, which may be at rest or in motion. Mathematically speaking, it is the vector difference between the velocities of two bodies.
Constant velocity: When the velocity of an object changes concerning time, neither in terms of magnitude nor in the terms of direction, i.e. both the magnitude of the velocity and the direction of motion remains constant/same.
Instantaneous velocity: The velocity of a moving object at any given moment is termed instantaneous velocity. Magnitude wise its value is the same as the speed of the object at that moment.
Differentiate between speed and velocity:
- Distance travelled by a body in unit time is called speed, and displacement covered by an object in unit time is known as velocity.
- Speed is a scalar quantity, whereas velocity is a vector quantity.
- (Difference between distance and displacement- Distance is a scalar quantity, i.e. it depends on the path taken by the body during its motion whereas, a displacement which is a vector quantity, depends only on the initial and the final position of the path taken by the body. The distance between two points can never be 0, although the displacement may.)
- Speed only provide the information as to how fast an object is moving, wherein velocity implies both the magnitude as well as the direction of motion
- The velocity of an object could be positive, negative or zero, but the speed of an object could never be a negative value (speed could be zero, i.e. the body is at rest).
- Speed may or may not be equal to the velocity of the body.
- The velocity of an object at any given instant of time during the move can be equal to or less than the body’s speed. Still, it can never be greater than the speed while vice versa is possible, I.e. speed of an object can be greater than the magnitude of the object’s velocity at a given point of time.
Test your knowledge
- A boy walks to his school at a distance of 6 km with a constant speed of 2.5 kmph and walks back with a constant speed of 3 kmph. Find his average speed throughout the journey.
- A person walks up a stalled escalator in 100 seconds. When just standing on the same moving escalator, he is carried in 80 sec. Find the time it would take him to walk up the moving escalator?
- A car moves from X to Y with uniform speed V1 and returns to Y with a V2. Find the average speed of this trip.
- A car covers the first half of the journey at 30 kmph and rests another half at a speed of 60 kmph. Find the average speed of the car through the complete journey.
- A farmer has to walk 500 m due south, 400 m due west and 300 due north to reach his field, find the average velocity of the man during the walk?
- A particle covers ¾’th of the circle of radius r in time t. find the average velocity of the particle in this time interval.
- A 200 m long train is moving with a uniform velocity of 50 kmph. Find the time taken by the train to cross a bridge of length 2000 m.
- During the first 20 min of a 90 min trip, a car has an average speed of 15 m/s. What should be the average speed for the remaining 70 minutes, so the car has an average speed of 25 m/s for the entire trip?
Conclusion
Hope you now have a clear understanding of the difference between speed and velocity. Practice and solve these questions to grasp these concepts at your hands.