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Chapter 2: Problem 214

The relation between time and displacement of a moving particle is given by \(t=2 \alpha x^{2}\) where \(\alpha\) is a constant. The shape of the graph \(\mathrm{x} \rightarrow \mathrm{y}\) is (A) parabola (B) hyperbola (C) ellipse (D) circle

Short Answer

Expert verified
The given equation is \(y = 2 \alpha x^2\) which is the equation of a parabola in the form of \(y = Ax^2 + Bx + C\). So, the answer is (A) parabola.

Step by step solution

01

Identify given variables

We are given the equation for time and displacement, where \(t = 2 \alpha x^2\) We need to find the relation between x and y.
02

Rewrite the equation

Since we are looking for a graph relationship between x and y, let's rewrite the equation by introducing y. We are given that x is the displacement and y is the time, so from the equation \(y = 2 \alpha x^2\)
03

Identifying the graph type

Now, let's examine the expression for y in terms of x to identify the type of graph: \(y = 2 \alpha x^2\) This is the equation of a parabola in the form of \(y = Ax^2 + Bx + C\), where A, B, and C are constants. In our case, A is equal to \(2\alpha\) and B and C equal to 0. So, the answer is (A) parabola.

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