Question

A particle moves so that its position as a function of time in MKS unit is $\overrightarrow{r}=\hat{i}+4t^2\hat{j}+t\hat{k}$. The trajectory of the particle is

• A. A parabola
• B. An ellipse
• C. A circle
• D. None of these

Answer 1

The correct option is A A parabola

Given,

$\overrightarrow{r}=\hat{i}+4t^2\hat{j}+t\hat{k}$

From the above equation,

$x=ct$

$t=\frac{x}{c}$. . . . . . . . . . . . (1)

$y=4t^2$

$y=4(\frac{x}{c}{)}^2$

$y=\left(\frac{4}{c^2}\right)x^2$

This is the equation of a parabola.

The correct option is A.