consider a function (d=t*t) where d=distance in metre and t=time in second if t=1sec ,then total distance covered (d=1m) if t=2sec ,then total distance covered (d=4m) if t=3sec ,then total distance covered (d=9m) now consider the speed in every second 1 when t=1sec distance covered=1m ,that means speed=1m/sec. 2 when t=2sec distance covered=4m ,that means speed=3m/sec.that means in this second 3m distance is covered and 1m is already covered in the first second. therefore total distance of 4m is covered when t=2second 3 when t=3sec distance covered=9m ,that means if in this second 5m distance is covered and we know 4m distance is already covered in 2seconds,then it will be possible that total 9m distance is covered here speed=5m/sec. now my question is that derivative of distance w.r.t to time gives instantaneous speed. here in this case the derivative is (2t),when t=2 then derivative at 2 is 4. it means instantaneous speed=4m/sec. but the speed is 3m/sec when t=2sec.so how can the derivative can give instantaneous speed?
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In this case, the motion is not uniform. So the distance cannot be calculated by subtracting from the previous.
Thus, the correct way to solve this question is by using derivatives.