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# Speed: Definition, Types, Unit

Why is the man walking on the road able to cover less distance in the same time compared to a car that is riding next to him? The reason is that the car travels at a greater speed compared to the man. Similarly, a fast runner covers a greater distance compared to a slow runner because the former has greater speed compared to the latter. Speed is a measure of how fast or how slow someone or something moves.

## What is Speed?

Speed can be defined as the ratio of the distance traveled (d) to the time taken (t). A car moving with a greater speed would be able to reach its destination faster compared to another car that is moving at a slower speed. Mathematically,

Speed is a scalar quantity. The unit of speed is

## Average Speed

The ratio of total distance traveled by a body to the total time taken by it to cover that distance is called the average speed.

A moving body always possesses a positive speed; speed can never be negative.
The slope of the displacement time graph gives aerage speed. Consider the following graph. If “sindicates displacement in time “t”,then between two points a and b,

## Instantaneous Speed

The instantaneous speed of a particle can be defined as the speed of a particle at a particular moment  of time .

i.e first derivative of s wrt time gives instantaneous speed.

Consider the following s-t graph which depicts a non-uniform motion. The tangent drawn to the curve at point P gives the slope at point P, ie. the value of instantaneous speed at that point.

## Relative Speed

Let us take for example, three athletes A,B and C who are running a race on the same track, parallel to each other. Now athlete A runs the fastest ,B is faster than C, however slower than A.

Fig shows three athletes A, B and C moving at different speeds. B is faster than C but is slower than A

Relative speed gives an idea how one body travels slower or faster in comparison to another. In this case, A moves at a greater speed compared to C, as A moves as compared to B.

The relative speed of A wrt B (when they are moving in the same direction) can be written as

Note: When A and B run in opposite directions, relative speed of A wrt B is

## Uniform and Non-uniform Motion

A motion is said to be uniform if the body covers equal distances in equal intervals of time. For eg. if a body covers 2 m of distance each second, the body is said to be in uniform motion. Whereas a motion is said to be non-uniform if the body covers unequal distances in equal intervals of time. A body in non-uniform motion is said to have acceleration.

## Practice Problems of Speed

Question 1. A body travels in a circular path of radius 7 m starting from A to B as shown in figure. The time taken to travel the distance AB is 2 s. What is the average speed of the body?

(a) 22 m/s (b) 44 m/s (c) 33 m/s (d) 11 m/s

The distance traveled along AB

Question 2. A car travels with a speed vu from X to Y. It returns from Y to X with a speed vd. What is the average speed of the car during this entire trip?

be the times taken by the car to go from X to Y and from Y to X .

Question 3. Person A runs eastwards with a speed of 2 m/s and person B runs westwards with a speed of 1 m/s. What is the relative speed of A wrt B ?

Answer: Since A and B run in opposite directions, relative speed= 2 m/s+1 m/s=3 m/s

Question 4. A car travels a total distance of d. If it travels the first half of the distance with a speed of 8 m/s; with what speed should it travel the second half so that the average speed comes out to be 12 m/s?

(a) 10 m/s (b)12 m/s (c)5 m/s (d)24 m/s

Let the car travel distance d/2 taking time t1 and the next part taking time t2

## FAQs of Speed

Question 1. What is speed? How is it different from velocity?

Answer: Speed is defined as the ratio of distance to the time taken. Speed is a scalar quantity. Velocity is displacement covered by an object divided by the time taken; and is a vector quantity.

Question 2. What is the unit of speed?

Distance traveled is the length, so it’s unit is m, and unit of time is s. So, unit of speed is ms-1.

Question 3. Can average velocity be greater than average speed?

Let’s say a body moves from A to B along the semicircle. Now we can clearly see that distance is greater than the magnitude of displacement. Distance = magnitude of displacement for a straight line motion. So, average velocity can never be greater than average speed.

Question 4. Does the speedometer show us average or instantaneous speed?

Answer: The speedometer shows the speed at a given time. So, the speedometer shows us instantaneous speed.

## NCERT Class 11 Physics Chapters

 Physical World Units and Measurements Motion in a Straight Line Motion in a Plane Laws of Motion Work Energy and Power Particles and Rotational Motion Gravitation Mechanical Properties of Solids Mechanical Properties in Liquids Thermal Properties of Matter Thermodynamics Kinetic Theory Oscillations Waves

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