Answer :
Final answer:
To calculate the capacitance required to store the kinetic energy of a 1270-kg electric car braking from 13.0 m/s to rest at 188 V, the energy equations for kinetic energy and a capacitor were used, resulting in a capacitance value of 6.07 F, which does not match the provided options. So, the correct option is 'None of the above'.
Explanation:
To determine the capacitance required to store the kinetic energy of a 1270-kg electric car as it brakes to a stop, we need to use the relationship between the car's kinetic energy and the energy stored in a capacitor. The kinetic energy (KE) of the car can be found using the equation KE = (1/2)mv2, where m is the mass of the car and v is its velocity. Thus, the kinetic energy of the car when braking from 13.0 m/s to rest is: KE = (1/2) × 1270 kg × (13.0 m/s)2 = 107,285 J.
The energy (E) stored in a capacitor is given by the equation E = (1/2)CV2, where C is the capacitance and V is the voltage. To find the capacitance, we set the kinetic energy equal to the energy stored in the capacitor and solve for C: 107,285 J = (1/2)C × (188 V)2.C = (2 × 107,285 J) / (188 V)2 = 6.07 F. However, this value is not among the options provided (a. 120 F, b. 150 F, c. 180 F, d. 200 F), suggesting a potential miscalculation, error in the provided answer options, or a misinterpretation of the question. It's important to double-check calculations and question parameters when answers do not align with given options.
