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if velocity is depending on time such that v=4-2t find out distance traveled by particle from 1 to 3s

Asked by gargpuneet989 25th June 2018, 5:42 PM
Answered by Expert
Answer:
begin mathsize 12px style V space equals space fraction numerator d x over denominator d t end fraction space equals space 4 space minus space 2 cross times t space space semicolon space space d x space equals space open parentheses 4 space minus space 2 cross times t close parentheses space d t
integral d x space equals integral subscript 1 superscript 3 open parentheses 4 space minus space 2 cross times t close parentheses space d t space equals space 0 space............... left parenthesis 1 right parenthesis
end style
Equation (1) shows the displacement = 0;
 
If we need to calculate the actual distance travelled from t=1 s to t=3 s ,
we need to separte the travel with +ve velocity and get the +ve displacement.
 
also we separate the travel with -ve velocity and get the -ve displacement.
Total distance travelled is sum of magnitude of displacements.
 
From given velocity-time relation,it can be seen that velocity becomes zero at t = 2;
 
hence actual distance travelled begin mathsize 12px style integral subscript 1 superscript 2 left parenthesis 4 minus 2 t right parenthesis d t space plus space open vertical bar integral subscript 2 superscript 3 left parenthesis 4 minus 2 t right parenthesis d t space close vertical bar space equals space 1 plus 1 space equals space 2 space m end style
Answered by Expert 25th June 2018, 11:17 PM
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