Question

A stone is projected from level ground at time t = 0, let $v_x$ and $v_y$ be the horizontal and vertical components of velocity at any time t ; x and y are displacements along horizontal and vertical from the point of projection at any time t. Then (Neglect air friction)

• A. $v_y-t$ graph is a straight line
• B. $x-t$ graph is a straight line passing through origin
• C. $y-t$ graph is a straight line passing through origin
• D. $v_x-t$ graph is a straight line

Answer 1

Answer: (A), (B), (D)

The correct options are
A $v_y-t$ graph is a straight line
B $x-t$ graph is a straight line passing through origin
D $v_x-t$ graph is a straight line

Let $v_{x}and{v}_y$ be horizontal and vertical components of velocity respectively at t = 0. Then, $v_y=u_y-gt$
Hence, $v_y-t$ graph is straight line.
$x=v_{x}t$
Hence, x - t graph is straight line passing through origin.
The relation between y and t is $y=u_{y}t-\frac{1}{2}g{t}^2$
Hence y-t graph is parabolic.
$v_x=constant$
Hence, $v_x-t$ graph is a straight line.