Question

What will be the shape of the x→y graph, if the relation between time and displacement of the moving body is t = 2αx2 where α is constant. (a) Circle (b) Staright line (c) Parabola (d) Hyperbola

Answer 1

Given:

the relation between time and displacement of the moving body is t = 2αx2 where α is constant.

To find:

Nature of x-t graph.

Calculation:

The supplied relationship between Displacement and Time is:

$\therefore \: t = 2 \alpha {x}^{2}$

$= > {x}^{2} = \dfrac{t}{2 \alpha }$

$= > x = \sqrt{ \dfrac{t}{2 \alpha } }$

Since $\alpha$ is a constant , hence:

$= > x \: \propto \: \sqrt{t}$

So , this type of relationship creates a PARABOLIC CURVE.

Graph:

$\boxed{\setlength{\unitlength}{1cm}\begin{picture}(8,8)\put(1,1){\vector(1,0){6}}\put(1,1){\vector(0,1){6}}\put(1,7.25){x}\put(7.25,1){t}\qbezier{(1,1)(4,6)(6,6.5)}\end{picture}}$

Answer 2

Answer:THE ANSWER IS A.

Explanation: