Question

Figure shows $(x,t),(y,t)$ diagram of a particle moving in $2-$dimensions.

If the particle has a mass of $500\text{g}$, the force acting on the particle is (Assume $x=t,y=t^2$ are equation of given graphs)

• A. $1\text{N}$ along $y-$ axis
• B. $1\text{N}$ along $x-$ axis
• C. $0.5\text{N}$ along $x-$ axis
• D. $0.5\text{N}$ along $y-$ axis

Answer 1

The correct option is A $1\text{N}$ along $y-$ axis

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 $a_x=\frac{d{v}_x}{dt}=0$.
Since $a_x=0$, force along $x-$ direction will be zero.
$v_y=\frac{dy}{dt}=2t$ and $a_y=2{\text{ms}}^{-2}$
The force acting on the particle is $F=m{a}_y=\left(0.5\text{kg}\right)\left(2{\text{ms}}^{-2}\right)=1\text{N}$ along $y-$ axis