ICSE Class 9 Answered
Laws of motion equations
Asked by Ramprasadramoji | 05 Sep, 2022, 18:44: PM
(1) Equation for velocity as a function of time.
Let us assume the motion is under uniform acceleration a.
Let u be initial velocity and v be the velocity after time t seconds.
Acceleration a is defined as rate of change of velocity
![begin mathsize 14px style a space equals space fraction numerator v space minus space u over denominator t end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/c5f2a1171584bd5aebf9c6bf8b70d217.png)
above expression is rewritten as
v = u + ( a × t ) ....................................(2)
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(1) Equation for displacement as a function of time.
Let S be the distance travelled in t seconds with uniform acceleration a .
Let u be the initial velocity at time t = 0.
if v is the final velocity after t seconds , then average velocity = ( v + u ) /2
distance travelled S = average velocity × time
![begin mathsize 14px style S space equals space fraction numerator left parenthesis v plus u right parenthesis over denominator 2 end fraction cross times t end style](https://images.topperlearning.com/topper/tinymce/cache/0130f2e76a0c2f731236da7e9ef5df8b.png)
If we substitute finale velocity v from eqn.(2) , then we get after simplifiaction
![begin mathsize 14px style S space equals space u space t space plus space left parenthesis 1 divided by 2 right parenthesis space a space t squared end style](https://images.topperlearning.com/topper/tinymce/cache/fec1b8ebd4e9250dcd8c9f0977016db7.png)
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(3) Equation for final velocity v as a function of distance travelled S
Let us consider equation(2) as given above
![begin mathsize 14px style S space equals space fraction numerator left parenthesis v plus u right parenthesis over denominator 2 end fraction cross times t end style](https://images.topperlearning.com/topper/tinymce/cache/0130f2e76a0c2f731236da7e9ef5df8b.png)
Let us substitute time t using eqn.(1)
![begin mathsize 14px style S space equals space fraction numerator left parenthesis v plus u right parenthesis over denominator 2 end fraction cross times fraction numerator left parenthesis v minus u right parenthesis over denominator a end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/da1a70f1d4a4a61741bfbe114f507478.png)
Above expression is simplified as
v2 = u2 + ( 2 a S )
Answered by Thiyagarajan K | 05 Sep, 2022, 19:59: PM
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