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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 ball is dropped from a height of 90 m on a floor. At each collision with the floor,  the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Height space from space which space the space ball space is space dropped comma space straight s space equals space 90 space straight m

Initial space velocity space of space the space ball comma space straight u space equals space 0 space straight m divided by straight s

Acceleration comma space straight a space equals space 9.8 space straight m divided by straight s squared space

Final space velocity space of space the space ball space equals space straight v space

Using space second space equation space of space motion comma space

Time left parenthesis straight t right parenthesis space taken space by space the space ball space to space hit space the space ground space is comma space

straight s space equals space ut space plus space 1 half at squared space

90 space equals space 0 space plus space space 1 half cross times 9.8 straight t squared space

straight t space equals space square root of 18.38 end root space equals space 4.29 space sec

Using space first space equation space of space motion comma space

Final space velcoity comma space straight v space equals space straight u space plus space at 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 0 space plus space 9.8 space cross times space 4.29 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 42.04 space straight m divided by straight s space

Rebound space velocity space of space the space
ball comma space straight u subscript straight r space equals space fraction numerator 9 straight v space over denominator 10 end fraction space equals space fraction numerator 9 cross times 42.04 over denominator 10 end fraction space equals space 37.84 space straight m divided by straight s

Time left parenthesis straight t right parenthesis space taken space by space the space ball space to space reach space straight a space maximum space
height space is comma space

Using space first space equation space of space motion comma space

straight v space equals space straight u subscript straight r space plus space at apostrophe space

0 space equals space 37.84 space plus space left parenthesis – space 9.8 right parenthesis space straight t apostrophe

straight t apostrophe space equals space minus 37.84 space divided by space minus 9.8 space equals space 3.86 space straight s space

Total space time space taken space by space the space
ball space equals space straight t space plus space straight t apostrophe space equals space 4.29 space plus space 3.86 space equals space 8.15 space straight s

Since comma space time space of space ascent space equals space time space of space descent comma space

Time space taken space by space the space ball space to space rebound space from space
the space floor space equals space 3.86 space straight s

Velocity space with space which space the space ball space rebounds
from space the space floor space equals space 9 cross times fraction numerator 37.84 over denominator 10 end fraction equals 34.05 space straight m divided by straight s

Total space time space taken space by space the space ball space from space second space
rebound space equals 8.15 space plus space 3.86 space equals space 12.01 space straight s 

Speed-time graph for the ball is as shown below: 



217 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. 
650 Views

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

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. 
657 Views

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. 
1986 Views