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2.Motion in Straight Line
hard
આપેલ આલેખ વેગ વિરુદ્ધ સ્થાનાંતર નો વક્ર દર્શાવે છે.તો નીચેનામાથી કયો આલેખ પ્રવેગ વિરુદ્ધ સ્થાનાંતર ના વક્ર માટે સાચો છે?
A
B
C
D
(IIT-2005)
Solution
(a) Given line have positive intercept but negative slope. So its equation can be written as
$v = – mx + {v_0}$…..(i) [where $m = \tan \theta = \frac{{{v_0}}}{{{x_0}}}$]
By differentiating with respect to time we get $\frac{{dv}}{{dt}} = – m\frac{{dx}}{{dt}} = – mv$
Now substituting the value of $v$ from eq. (i) we get $\frac{{dv}}{{dt}} = – m[ – mx + {v_0}] = {m^2}x – m{v_0}$
$\therefore a = {m^2}x – m{v_0}$
i.e. the graph between $a$ and $x$ should have positive slope but negative intercept on $a-$axis. So graph $(a) $ is correct.
Standard 11
Physics
