Question

A body is projected horizontally from a point above the ground. The motion of body is defined as $x=2t;y=2t^2$ where $x\text{and}y$ are horizontal and vertical displacement respectively at time $t$.Which of the following is/are true?

• A. The trajectory of the body is a parabola
• B. The trajectory of the body is a straight line
• C. The velocity vector at time $t$ is
  $2\hat{i}+4t\hat{j}$
• D. The acceleration vector at time $t$ is $4\hat{j}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A The trajectory of the body is a parabola
C The velocity vector at time $t$ is
$2\hat{i}+4t\hat{j}$
D The acceleration vector at time $t$ is $4\hat{j}$

Given,
$x=2t;y=2t^2$
Eliminating $t$ we get
$y=\frac{x^2}{2}$
So it is parabola.
$V_x=\frac{dx}{dt}=2$
$V_y=\frac{dy}{dt}=4t$
So, the velocity at any time $t$ is given by
$V=2\hat{i}+4t\hat{j}$
Now similarly,
$a_x=\frac{d{V}_x}{dt}=0$
$a_y=\frac{d{V}_y}{dt}=4$
So acceleration vector is $a=4\hat{j}$