Question

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

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

Answer 1

Answer: (A)

Since the graph between $x$ and $t$ is a straight line and passing through the 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
$F=m{a}_y$ $=\left(0.5kg\right)$ $\left(2m{s}^{-2}\right)$ $=1N$ along $y$-axis