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 $500\, g,$ 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)

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 $ $y=t^{2}$
$\therefore \quad$ $v_{x}=\frac{d \,x}{d \, t}=1$ and $a_{x}=\frac{d v_{x}}{d t}=0$
and $v_{y}=\frac{d \, y}{d \,t}=2 t $ and $a_{y}=2 m\, s^{-2}$
The force acting on the particle is
$F=ma_{y}$ $=\left(0.5\, kg\right)$ $\left(2\,m\,s^{-2}\right)$ $=1 \, N $ along $y$-axis