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

1.	Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions.If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.
Answer» From graph (a) As, v_x = \(\frac{dx}{dt}\)= \(\frac{2}{2}\) = 1 m/s a_x = \(\frac{dv_x}{dt}\) = 0 from (b), y = t² v_y = \(\frac{dy}{dt}\) = 2t a_y = \(\frac{dv_y}{dt}\) = 2 F_y = ma_y = 0.5 × 2 = 1N (toward y-axis) F_x = 0.5 × 0 = 0 N F = \(\sqrt{F^2_s+F^2_y}=\sqrt{0^2+1^2}\) F = 1 N (towards Y-axis)

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

Answer»

From graph (a)

As, v_x = \(\frac{dx}{dt}\)= \(\frac{2}{2}\) = 1 m/s

a_x = \(\frac{dv_x}{dt}\) = 0

from (b), y = t²

v_y = \(\frac{dy}{dt}\) = 2t

a_y = \(\frac{dv_y}{dt}\) = 2

F_y = ma_y

= 0.5 × 2 = 1N (toward y-axis)

F_x = 0.5 × 0 = 0 N

F = \(\sqrt{F^2_s+F^2_y}=\sqrt{0^2+1^2}\)

F = 1 N (towards Y-axis)