Answer:
a) Θ = ω₀*t + ½αt² To complete first revolution 2π rads = 0*t + ½αt² and to complete the first and second combined 4π rads = 0*t + ½α(t+0.810s)² Divide second by first: 2 = (t + 0.810s)² / t² This is quadratic in t and has roots at t = -0.336 s ← ignore and t = 1.96 s ◄ b) Use either equation from above: 2π rads = 0*t + ½α(1.96s)² α = 3.27 rad/s² ◄ Hope this helps!
Explanation:
Answer:
2.5 seconds
Explanation:
s(t) = -16t^2 + 80t + 384
for
0≤t≤8
First we differentiate s(t) to get s'(t)
s'(t) = -32t + 80
Let us then find the critical point; thus we will equate s'(t) to zero and then search for values where s'(t) is undefined
s'(t) = -32t + 80 = 0
t = 80/32
t = 2.5 sec
Let us evaluate s at the critical points and end points
s(0) = -16(0)^2 + 80(0) + 384 = 384
s(2.5) = -16(2.5)^2 + 80(2.5) + 384 = 684
s(8) = -16(8)^2 + 80(8) + 384 = 0
Thus, the stone attains it maximum height of 684ft at at t=2.5s
Answer:
The value is 
Explanation:
From the question we are told that
The molar mass of hydrazine is 
The initial temperature is 
The final temperature is 
The specific heat capacity is ![c_h = 0.099 [kJ/(mol K)] = 0.099 *10^3 J/(mol/K)](https://tex.z-dn.net/?f=c_h%20%20%3D%20%200.099%20%5BkJ%2F%28mol%20K%29%5D%20%3D%200.099%20%2A10%5E3%20J%2F%28mol%2FK%29)
The power available is 
The mass of the fuel is 
Generally the number of moles of hydrazine present is

=> 
=> 
Generally the quantity of heat energy needed is mathematically represented as
=>
=>
Generally the time taken is mathematically represented as

=> 
=> t = 2480505.6377 s
Converting to hours

=> 
π=iMRT
Where, π is Osmotic pressure,
i=1 for non-electrolytes,
M is molar concentration of dissolved species (units of mol/L)
R is the ideal gas constant = 0.08206 L atm mol⁻¹K⁻¹,
T is the temperature in Kelvin(K),
Here, to calculate M convert into standard units mg tog, ml to L, c to Kelvin
M= (
*10⁻³ )/ 0.175 =(5.987 *10⁻⁵)mol / 0.175L = 34.21*10⁻⁵ mol/L
π=iMRT=(1)*(34.21*10⁻⁵)*(0.08206)*(298.15)=837×10⁻⁵= 8.37×10⁻³ atm
=6.36 torr
(1 atm=760 torr, 1 Kelvin =273.15 °C, 1L=1000ml, 1g=1000mg)