Question

Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions. If the particle has a mass of 500 g, the force acting on the particle is

• A. 1 N along y-axis
• B. 1 N along x-axis
• C. 0.5 N along x-axis
• D. 0.5 N along y-axis

Answer 1

Answer: (A)

1 N along y-axis

Since the graph between x and t the is a straight line and passing through origin.
$\therefore$ x=t
Since the graph between y and t is a parabola,
$\therefore y=t^2$
$\therefore v_x=\frac{dx}{dt}=1$ and $a_x=\frac{d{v}_x}{dt}=0$

and $v_y=\frac{dy}{dt}=2t$ and $a_y=2m{s}^{-2}$

The force acting on the particle is
$F=m{a}_y=\left(0.5kg\right)\left(2m{s}^{-2}\right)$= 1 N along y-axis