Question

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

Answer 1

$\text{Step1: Find the value of}{a}_x\text{for}x-t\text{graph}$.

Since the graph between $x$ and $t$ is a straight line and passing through origin.

Therefore, $x=t$

As we know,
$v=\frac{dx}{dt}$ and $a=\frac{dv}{dt}$

Then,
$v_x=\frac{dx}{dt}=1$ and $a_x=\frac{d{v}_x}{dt}=0$

The force acting on the particle is
$F=m{a}_x$

$F=0$

$\text{Step2: Find the value of}{a}_y\text{for}y-t\text{graph}$

Since the graph between $y$ and $t$ is a parabola,

$\therefore y=t^2$

As we know,

$v=\frac{dx}{dt}$ and $a=\frac{dv}{dt}$

Then,
$v_y=\frac{dy}{dt}=2t$

and $a_y=2m/s^2$

The force acting on the particle is

$F=m{a}_y=\left(0.5kg\right)\left(2\frac{m}{s^2}\right)$

$F=1N$ along $y-$ axis

$\text{Final Answer}:F=0,F=1N$ along $y-$ axis