Question

A body moves along x - axis with velocity $\mho$. If the plot $\mho$-x is ellipse with major axis 2A and minor axis 2$\mho$then of maximum acceleration is:

Answer 1

the equation of ellipse is :- $\frac{v^2}{{\mho }^2}+\frac{x^2}{A^2}=1$

this equation represents a linear $SHM$ along $x-$axis,with amplitude $=A$ and maximum velocity =$\mho$

we know, maximum velocity for $SHM$:

$v_{max}=\mho =AW$ ($w$,angular velocity of $SHM$)

$\Rightarrow w=\frac{\mho }{A}----\left(i\right)$

so, maximum acceleration is given by:

$a_{max}=A{w}^2=A{\left(\frac{\mho }{A}\right)}^2$

$a_{max}=\frac{{\mho }^2}{A}$ [from $\left(i\right)$]