Two forces, F, = (-4.00î – 3.95j) N and F, = (-3.95î - 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at 1 coordinates (+1.95 m, +4.05 m). (a) What are the components of the particle's velocity at t = 11.1 s? m/s (b) In what direction is the particle moving at t = 11.1 s? ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.1 s? AF = m (d) What are the coordinates of the particle at t = 11.1 s? y = m

Two forces, F, = (-4.00î – 3.95j) N and F, = (-3.95î - 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at 1 coordinates (+1.95 m, +4.05 m). (a) What are the components of the particle's velocity at t = 11.1 s? m/s (b) In what direction is the particle moving at t = 11.1 s? ° counterclockwise from the +x-axis (c) What displacement does the particle undergo during the first 11.1 s? AF = m (d) What are the coordinates of the particle at t = 11.1 s? y = m

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Question

Two forces, F
:(-4.00î – 3.95ĵ) N and F, = (-3.95î – 4.95j) N, act on a particle of mass 1.90 kg that is initially at rest at
1
coordinates (+1.95 m, +4.05 m).
(a) What are the components of the particle's velocity at t = 11.1 s?
m/s
(b) In what direction is the particle moving at t = 11.1 s?
° counterclockwise from the +x-axis
(c) What displacement does the particle undergo during the first 11.1 s?
(d) What are the coordinates of the particle at t = 11.1 s?
X =
m
y =

Expert Solution

Step 1

Solution:

Given

$\overset{⇀}{F_{1}} = (- 4.00 \overset{⏜}{i} - 3.95 \overset{⏜}{j}) N \overset{⇀}{F_{2}} = (- 3.95 \overset{⏜}{i} - 4.95 \overset{⏜}{j}) N mass m = 1.90 kg coordinates = (+ 1.95 m + 4.05 m)$

(a) Net force on the particle is

$\overset{⇀}{F} = \overset{⇀}{F_{1}} + \overset{⇀}{F_{2}}$

$\overset{⇀}{F} = (- 4 \overset{⏜}{i} - 3.95 \overset{⏜}{j}) + (- 3.95 \overset{⏜}{i} - 4.95 \overset{⏜}{j}) \overset{⇀}{F} = (- 7.95 \overset{⏜}{i} - 8.9 \overset{⏜}{j}) N$

we know that

acceleration= $\overset{⇀}{a} = \frac{\overset{⇀}{F}}{m} = \frac{(- 7.95 \overset{⏜}{i} - 8.9 \overset{⏜}{j}) N}{1.90 kg}$

$∴ \overset{⇀}{a} = (- 4.18 \overset{⏜}{i} - 4.68 \overset{⏜}{j}) m / s^{2}$

So,

$\overset{⇀}{v} = \overset{⇀}{u} + \overset{⇀}{at} \overset{⇀}{v} = 0 + (- 4.18 \overset{⏜}{i} - 4.68 \overset{⏜}{j}) m / s^{2} (11.1 s) \overset{⇀}{v} = (- 46.39 \overset{⏜}{i} - 51.94 \overset{⏜}{j}) m / s$