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ICSE Class 9 Answered

Laws of motion equations 

Asked by Ramprasadramoji | 05 Sep, 2022, 06:44: PM
Expert Answer
(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    ......................................(1)
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  ..................................(3)
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 ..................................(3)
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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
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
Above expression is simplified as
 
v2 = u2 + ( 2 a S )
 
Answered by Thiyagarajan K | 05 Sep, 2022, 07:59: PM
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