Final answer:
The total acceleration of an object with a charge of 2 C and a mass of 0.5 kg moving through an electromagnetic field with specific electric and magnetic field components is 8ax+8ay m/s^2. The acceleration is calculated using the Lorentz force which, in this case, only includes the contribution from the electric field since the cross product of the velocity and magnetic field is zero.
Step-by-step explanation:
To calculate the total acceleration of the object with a charge of 2 C and a mass of 0.5 kg moving through an electromagnetic field with an electric field E = 2ax+2ay V/m and a magnetic field B = 4ax Wb/m^2, we must consider both the electric and magnetic contributions to the acceleration. The Lorentz force F on the object is given by the equation F = qE + q(v × B), where q is the charge of the object, v is the velocity, and × denotes the cross product.
The electric force is Fe = qE. Substituting the given values, we get Fe = (2 C)(2ax+2ay) N = 4ax+4ay N. The magnetic force is Fb = q(v × B). Using the given velocity u = 3ax+4az m/s and the magnetic field B = 4ax Wb/m^2, the cross product gives us Fb = q[(3ax+4az) × 4ax]. However, since the velocity and the magnetic field both have the ax component, their cross product will be zero, and therefore the magnetic force Fb is zero.
Therefore, the total force acting on the object is simply the electric force Fe, and the total acceleration a can be obtained using Newton's second law F = ma. Substituting F with Fe and solving for a gives us a = (4ax+4ay) N / (0.5 kg) = 8ax+8ay m/s^2. This is the total acceleration of the object at that instant of time.