The position of the particle is given by:
x(t) = t³ - 12t² + 21t - 9
Differentiate x(t) with respect to t to find the velocity x'(t):
x'(t) = 3t² - 24t + 21
Differentiate x'(t) with respect to t to find the acceleration x''(t):
x''(t) = 6t - 24
Answer:
Radius, 
Explanation:
It is given that,
Magnetic field, B = 0.275 T
Kinetic energy of the electron, 
Kinetic energy is given by :


v = 1037749.04 m/s
The centripetal force is balanced by the magnetic force as :




So, the radius of the circular path is
. Hence, this is the required solution.
Answer:
The change in internal energy of the system is -17746.78 J
Explanation:
Given that,
Pressure 
Remove heat 
Radius = 0.272 m
Distance d = 0.163 m
We need to calculate the internal energy
Using thermodynamics first equation
...(I)
Where, dU = internal energy
Q = heat
W = work done
Put the value of W in equation (I)

Where, W = PdV
Put the value in the equation


Hence, The change in internal energy of the system is -17746.78 J