Respuesta :
Answer:
x = 1,185 m , t = 4/3 s , F = - 4 N
Explanation:
For this exercise we use Newton's second law
F = m a = m dv /dt
β - α t = m dv / dt
dv = (β – α t) dt
We integrate
v = β t - ½ α t²
We evaluate between the lower limits v = v₀ for t = 0 and the upper limit v = v for t = t
v-v₀ = β t - ½ α t²
the farthest point of the body is when v = v₀ = 0
0 = β t - ½ α t²
t = 2 β / α
t = 2 4/6
t = 4/3 s
Let's find the distance at this time
v = dx / dt
dx / dt = v₀ + β t - ½ α t2
dx = (v₀ + β t - ½ α t2) dt
We integrate
x = v₀ t + ½ β t - ½ 1/3 α t³
x = v₀ 4/3 + ½ 4 (4/3)² - 1/6 6 (4/3)³
The body comes out of rest
x = 3.5556 - 2.37
x = 1,185 m
The value of force is
F = β - α t
F = 4 - 6 4/3
F = - 4 N
The distance covered can be found by deriving the function for distance,
from the function of force.
First part; 1.185 meters
Second part; 4/3 seconds
Third part; -4 N
Reasons:
First part;
The horizontal force acting on the Fₓ(t) = β - α·t
By integration, we have, distance reached, x(t) = 2·t² - t³
At the maximum point, we have;
[tex]\dfrac{d(x)}{dt} = 4\cdot t- 3 \cdot t^2 = 0[/tex]
Therefore;
4·t - 3·t² = 0
(4 - 3·t)·t = 0
t = 4/3
The largest positive value of x = 2 ×(4/3)² -(4/3)³ = [tex]1.\overline{185}[/tex]
The largest positive value of x ≈ 1.185 meters
Second part:
The time it takes the block to reach the maximum point, t = 4/3 seconds
Third part:
The magnitude of the force, Fₓ(4/9) = 4 - 6×(4/3) = -4
The magnitude of the force when x = 1.185 meters, Fₓ = -4 N.
Learn more here:
Learn more here:
https://brainly.com/question/14126224
