In acceleration time graph how speed finding by area enclosed under the graph . detail understanding

Asked by swainanirudha1 | 13th Nov, 2018, 12:35: AM

Expert Answer:

Acceleration is defined as rate of change of speed. Let a(t) is acceleration which is varying with time.
 
Then we have, begin mathsize 12px style fraction numerator d v over denominator d t end fraction space equals space a left parenthesis t right parenthesis space............... left parenthesis 1 right parenthesis end style
it is assumed in eqn.(1), Speed v also varying with time.
 
Eqn.(1) can be written as, begin mathsize 12px style d v space equals space a left parenthesis t right parenthesis d t space...................... left parenthesis 2 right parenthesis end style
 
If change in speed is from vi to vf in interval of time between ti and tf ,
we write,  begin mathsize 12px style v subscript f space minus space v subscript i space equals space integral subscript v subscript i end subscript superscript v subscript f end superscript d v space equals space integral subscript t subscript i end subscript superscript t subscript f end superscript a left parenthesis t right parenthesis d t space space................. left parenthesis 3 right parenthesis end style
extreme RHS of eqn.(3) is integration of time varying acceleration function within the time interval ti and tf .
Hence as shown in figure the change in speed can be calculated as area under the curve, if acceleration is plotted against time

Answered by Thiyagarajan K | 13th Nov, 2018, 07:01: AM

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