The electric field at (x,y,z) its equal to the negative of the gradient if the electric potential.
We have
V(x, y, z) = 2x² - 3y² + 5z
so
E(x, y, z) = -grad(V) = -(dV/dx i + dV/dy j + dV/dz k)
where d/d(variable) is meant to be a partial derivative with respect to that variable. The partial derivatives are
dV/dx = 4x
dV/dy = -6y
dV/dz = 5
and so the electric field at any point is
E(x, y, z) = -4x i + 6y j - 5k
and at (3, 4, 5) it is
E(3, 4, 5) = -12i + 24j - 5k
Answer:
C) According to the second law of thermodynamics, not all energy from the burnt fuel is used to do work on the piston. It also produces heat which warms other parts of the car.
Explanation:
A) According to the fourth law of thermodynamics, the temperature of the other parts of the car increases due to the coolant used for the engine.
B) According to the first law of thermodynamics, the hood of the car heats up using heat from the surroundings in-order to achieve thermal equilibrium with the engine.
C) According to the second law of thermodynamics, not all energy from the burnt fuel is used to do work on the piston. It also produces heat which warms other parts of the car.
D) According to the third law of thermodynamics, the increase in the velocity of the car changes the entropy of the tires. To balance this change, the temperature of the other parts is increased.
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Answer:
The time taken by the car to accelerate from a speed of 24.6 m/s to a speed of 26.8 m/s is 0.84 seconds.
Explanation:
Given that,
Acceleration of the car, 
Initial speed of the car, u = 24.6 m/s
Final speed of the car, v = 26.8 m/s
We need to find the time taken by the car to accelerate from a speed of 24.6 m/s to a speed of 26.8 m/s. The acceleration of an object is given by :
t = 0.84 seconds
So, the time taken by the car to accelerate from a speed of 24.6 m/s to a speed of 26.8 m/s is 0.84 seconds. Hence, this is the required solution.
