Given: A rod
ABat t= tA XA=xA
at t=tB XB=xB
To Find: The Length of rod AB.
Formula used: v=△x△t
△x : difference in initial & final position of a point in rod.
△t : difference in initial & final time.
Solution:Let us assume that length of rod AB=l ; and tB > tA
Now, according to this question.
△t=tB−tA (iftB>tA)--------------------(1)
Hence, Let us take the front end of the rod.
So, distance travelled by front end of the rod will be △x;
at t=tA XA=xA
t=tB XA=xB+l
Hence, △XA=xB+l−xA--------(2)
So from the formula given:
v=△x△t------(3)
Hence we will substitute
eq(1) & eq(2) in eq(3) we get:
v=xB+l−xAtB−tA
So by solving the above equation:
(tB−tA)v =xB+l−xA
l=(tB−tA)v+xA−xB