Question

Two forces, vector F 1 = (−4.05î − 5.85ĵ) N and vector F 2 = (−3.55î − 6.90ĵ) N,

act on a particle of mass 2.40 kg that is initially at rest at coordinates
(−2.40 m, −4.05 m).
(a) What are the components of the particle's velocity at t = 11.8 s?
vector v =
m/s
(b) In what direction is the particle moving at t = 11.8 s?
° counterclockwise from the +x-axis
(c) What displacement does the particle undergo during the first 11.8 s?
Δvector r = m
(d) What are the coordinates of the particle at t = 11.8 s?
x = m
y = m

Answer 1

Newton's second law and kinematic equations are applied to find the velocity, direction of movement, displacement, and final coordinates of a particle influenced by two forces at a specific time.

Step-by-step explanation:

To solve for the components of the particle's velocity at a specific time under the influence of two forces, we will use Newton's second law, which states that the net force applied on an object is equal to the mass of the object multiplied by its acceleration (\( F = ma \)). First, we calculate the net force acting on the object by summing the individual forces vector \( F_1 \) and vector \( F_2 \). Then, we find the net acceleration using the net force and the mass of the object. Next, we use the kinematic equation for velocity, which is the initial velocity plus the acceleration multiplied by time (\( v = v_0 + at \)).

To find the direction in which the particle is moving, we would need to compute the angle of the velocity vector with respect to the positive x-axis. Lastly, to determine the displacement and final coordinates of the particle, we can integrate the velocity with respect to time or use kinematic equations if the acceleration is constant.