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

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

CBSE | Class 11 | Laws of Motion | ncert exemplar | Physics

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

For graph a)
$\begin{array}{l} v_{x}=d x / d t=2 / 2=1 \mathrm{~m} / \mathrm{s} \\ a_{x}=d^{2} x / d t^{2}=d v_{x} / d t=0 \end{array}$
For graph b)
$\begin{array}{l} y=t^{2} \\ v_{y}=d y / d t=2 t \\ a_{y}=d v_{y} / d t=2 \end{array}$
Therefore, $F_{y}=m a_{y}$
$\mathrm{m}=500 \mathrm{~g}=0.5 \mathrm{~kg}$
$\begin{array}{l} F_{y}=(0.5)(2)=1 \mathrm{~N} \text { towards } y \text {-axis } \\ F_{x}=(0.5)(0)=0 \mathrm{~N} \end{array}$
Therefore,
$F=\sqrt{F_{x}^{2}+F_{y}^{2}}=\sqrt{0^{2}+1^{2}}=\sqrt{1}$
Therefore, $F=1 \mathrm{~N}$ towards $y$ -axis.