Answer:
A) 3.13 m/s
B) 5.34 N
C) W = 26.9 J
Explanation:
We are told that the position as a function of time is given by;
x(t) = αt² + βt³
Where;
α = 0.210 m/s² and β = 2.04×10^(−2) m/s³ = 0.0204 m/s³
Thus;
x(t) = 0.21t² + 0.0204t³
A) Velocity is gotten from the derivative of the displacement.
Thus;
v(t) = x'(t) = 2(0.21t) + 3(0.0204t²)
v(t) = 0.42t + 0.0612t²
v(4.5) = 0.42(4.5) + 0.0612(4.5)²
v(4.5) = 3.1293 m/s ≈ 3.13 m/s
B) acceleration is gotten from the derivative of the velocity
a(t) = v'(t) = 0.42 + 2(0.0612t)
a(4.5) = 0.42 + 2(0.0612 × 4.5)
a(4.5) = 0.9708 m/s²
Force = ma = 5.5 × 0.9708
F = 5.3394 N ≈ 5.34 N
C) Since no friction, work done is kinetic energy.
Thus;
W = ½mv²
W = ½ × 5.5 × 3.1293²
W = 26.9 J
Answer:
Convection currents are the result of different heating. Lighter material (warm) rises while heavier (cold) material sinks. This movement of the materials is what causes convection currents! (BTW, it happens in water, in the atmosphere, and in the mantle of Earth!
Explanation:
I hope this helps a little! :)
Steel is more elastic than rubber<span> because </span>steel<span> comes back to its original shape faster </span>than rubber<span> when the deforming forces are removed, hope it helps :)</span>
Answer:
The level of the root beer is dropping at a rate of 0.08603 cm/s.
Explanation:
The volume of the cone is :
Where, V is the volume of the cone
r is the radius of the cone
h is the height of the cone
The ratio of the radius and the height remains constant in overall the cone.
Thus, given that, r = d / 2 = 10 / 2 cm = 5 cm
h = 13 cm
r / h = 5 / 13
r = {5 / 13} h
Also differentiating the expression of volume w.r.t. time as:
Given: 
= -4 cm³/sec (negative sign to show leaving)
h = 10 cm
So,
<u>The level of the root beer is dropping at a rate of 0.08603 cm/s.</u>
