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Motion in Straight Line

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h-1. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h-1. What is the
(a) magnitude of average velocity, and

(b) average speed of the man over the interval of time
(i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min ?
[Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !]

Time space taken space by space the space man space to space reach
market space from space home comma space straight t subscript 1 space equals space fraction numerator 2.5 over denominator 5 end fraction equals 1 half straight h space equals space 30 space min

Time space taken space by space the space man space to space reach
home space from space the space market comma space straight t subscript 2 space equals space fraction numerator 2.5 over denominator 7.5 end fraction equals 1 third straight h space equals space 20 space min

Total space time space taken space in space the space whole space journey space equals space 30 space plus 20 space equals space 50 space min

straight i right parenthesis thin space bold 0 bold space bold to bold space bold 30 bold space bold min

Average space velocity space equals space Displaceement over time space equals space fraction numerator 2.5 over denominator begin display style bevelled 1 half end style end fraction space equals space 5 space km divided by hr

Average space speed space equals fraction numerator space Distance over denominator Time space end fraction equals fraction numerator space 2.5 over denominator left parenthesis 1 divided by 2 right parenthesis end fraction space equals space 5 space km divided by straight h
ii right parenthesis thin space bold 0 bold space bold to bold space bold 50 bold space bold min
Time space equals space 50 space min space equals space 50 over 60 space equals space 5 divided by 6 space straight h space
Net space displacement space equals space 0
Total space distance space equals space 2.5 space plus space 2.5 space equals space 5 space km

Average space velocity space equals fraction numerator space Displacement over denominator Time space end fraction space equals space 0

space Average space speed space equals space fraction numerator Distance over denominator space Time end fraction space equals fraction numerator space 5 over denominator left parenthesis 5 divided by 6 right parenthesis end fraction space equals space 6 space km divided by straight h space

iii right parenthesis thin space bold 0 bold space bold to bold space bold 40 bold space bold min

Speed space of space the space man space equals space 7.5 space km divided by straight h
Distance space travelled space in space first space 30 space min space equals space 2.5 space km

Distance space travelled space by space the space man space left parenthesis from space market space to space home right parenthesis
space in space the space next space 10 space min space equals space 7.5 space cross times 10 over 60 equals 1.25 space km
Net space displacement space equals space 2.5 space – space 1.25 space equals space 1.25 space km

Total space distance space travelled space equals space 2.5 space plus space 1.25 space equals space 3.75 space km space

Average space velocity space equals space Displacment over time
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1.25 over denominator left parenthesis 40 divided by 60 right parenthesis end fraction space equals space 1.875 space km divided by hr space

Average space Speed space equals space Distance over time space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator left parenthesis 3.75 right parenthesis over denominator left parenthesis 40 divided by 60 right parenthesis end fraction space equals space 5.625 space km divided by hr
347 Views

What is the most essential thing to study the motion of a body?

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion. 
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What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest. 
1215 Views

What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion. 
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Is absolute rest or absolute motion possible?

Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion. 
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Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself. 
746 Views