Answer:
(a) Equation of straight
line is given by
\[y=mx+c\]
Where, m is the
slop and c is the intercept on y axis.
In the given graph, \[y=\upsilon
,\]slope \[=\left( -\frac{{{\upsilon }_{0}}}{{{x}_{0}}} \right)\]
And intercept \[={{\upsilon
}_{0}}\]
\ \[\upsilon \,=\,\left(
-\frac{{{\upsilon }_{0}}}{{{x}_{0}}} \right)\,x\,+\,{{\upsilon }_{0}}\] ?
(i)
(b) \[a\,=\frac{d\upsilon
}{dt}\,\,=\,\,\left( -\frac{{{\upsilon }_{0}}}{{{x}_{0}}}
\right)\frac{dx}{dt\,}\,=\left( -\frac{{{\upsilon }_{0}}}{{{x}_{0}}}
\right)\upsilon \]
Using eqn. (i), we get
\[a\,=\,\left(
-\frac{{{\upsilon }_{0}}}{{{x}_{0}}} \right)\left[ \left( -\frac{{{\upsilon
}_{0}}}{{{x}_{0}}} \right)x+{{\upsilon }_{0}} \right]\]
\[\,=\,\left(
\frac{\upsilon _{0}^{2}}{x_{0}^{2}} \right)x\,-\,\upsilon _{0}^{2}\,\]
Graph between \['a'\] and \['x'\]
is shown in figure
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