A particle is moving in $x-y$ plane with its $x$ and $y$ co-ordinates varying with time as, $x=2 t$ and $y=10t-16t^2$. Find trajectory of the particle.

Given, 

$$\begin{gathered} x=2t \\ t=\frac{x}{2} \end{gathered}$$

Now, $y=10t-16t^2$.

Substituting value of t in this equation we have, 

$y=10\left(\frac{x}{2}\right)-16{\left(\frac{x}{2}\right)}^2$

or $y=5x-4x^2$

This is the required equation of trajectory of the particle. This is a quadratic equation. Hence, the path of the particle is a parabola.