A particle moves along the x axis. It is initially at the position 0.280 m, moving with velocity 0.080 m/s and acceleration -0.240 m/s2. Suppose it moves with constant acceleration for 3.10 s.

(a) Find the position of the particle after this time.

(b) Find its velocity at the end of this time interval.

Next, assume it moves with simple harmonic motion for 3.10 s and x = 0 is its equilibrium position.

(c) Find its position.

(d) Find its velocity at the end of this time interval.

a and b require kinematic questions and are therefore easy. anyone know how to do c and d?

To solve the given problem, we need to use the equations of motion. Specifically, we will use the kinematic equations for linear motion with constant acceleration, as well as equations for simple harmonic motion.

(a) To find the position of the particle after 3.10 s with constant acceleration, we can use the equation:

x = x₀ + v₀t + (1/2)at²

where x₀ is the initial position, v₀ is the initial velocity, t is the time, and a is the acceleration.

Given:
x₀ = 0.280 m (initial position)
v₀ = 0.080 m/s (initial velocity)
t = 3.10 s (time)
a = -0.240 m/s² (acceleration)

Substituting these values into the equation, we get:

x = 0.280 + 0.080(3.10) + (1/2)(-0.240)(3.10)²

Simplifying the equation, we find:

x ≈ 0.280 + 0.248 + (-0.361)

x ≈ 0.167 m

Therefore, the position of the particle after 3.10 s is approximately 0.167 m.

(b) To find the velocity of the particle at the end of 3.10 s with constant acceleration, we can use the equation:

v = v₀ + at

Given:
v₀ = 0.080 m/s (initial velocity)
t = 3.10 s (time)
a = -0.240 m/s² (acceleration)

Substituting these values into the equation, we get:

v = 0.080 + (-0.240)(3.10)

Simplifying the equation, we find:

v ≈ 0.080 + (-0.744)

v ≈ -0.664 m/s

Therefore, the velocity of the particle at the end of 3.10 s is approximately -0.664 m/s.

(c) To find the position of the particle after 3.10 s with simple harmonic motion, we can use the equation:

x = A * cos(ωt)

where A is the amplitude and ω is the angular frequency.

However, we are not given the values for A or ω. Without this information, it is not possible to determine the exact position of the particle.

(d) Similarly, without knowing the amplitude (A) and the angular frequency (ω), we cannot determine the exact velocity of the particle at the end of 3.10 s with simple harmonic motion.