Answer:
x(t) = ⅟₁₀₈t⁴ + 10t + 24
v(t) = ⅟₂₇t³ + 10
Explanation:
a(t) = C₁t²
velocity is the integral of acceleration
v(t) = ⅓C₁t³ + C₂
position is the integral of velocity
x(t) = (⅟₁₂C₁)t⁴ + C₂t + C₃
x(0) = 24 = (⅟₁₂C₁)0⁴ + C₂0 + C₃
C₃ = 24
x(6) = 96 = (⅟₁₂C₁)6⁴ + C₂6 + 24
72 = 108C₁ + 6C₂
C₂ = 12 - 18C₁
v(6) = 18 = ⅓C₁6³ + C₂
18 = 72C₁ + C₂
18 = 72C₁ + (12 - 18C₁)
6 = 54C₁
C₁ = 1/9
C₂ = 12 - 18(1/9)
C₂ = 10
Answer:
1.2 s
Explanation:
Given:
v₀ = 8.0 m/s
v = -4.0 m/s
a = -10 m/s²
Find: t
v = at + v₀
(-4.0 m/s) = (-10 m/s²) t + (8.0 m/s)
t = 1.2 s
Answer:
If you take the first example of the walk around the desk, it should be apparent that sometimes the distance is the same as the magnitude of the displacement. ... Since the displacement is measured along the shortest path between two points, its magnitude is always less than or equal to the distance.
The first collision because a greater amount of momentum must be taken and used in order to push the cart back, giving it a greater mass and impulse
Answer:
0.477 Hz
2.09 s
Explanation:
y = A sin(ωx − φ)
A is the amplitude, ω is the angular frequency, and φ is the phase shift.
ω = 3 rad/s
f = ω / 2π ≈ 0.477 Hz
T = 1/f ≈ 2.09 s
