Final answer:
To calculate the average current drawn by the bus, we first determine the kinetic energy at the final velocity. Then, considering the 40% efficiency and total energy input, we find the power consumed and ultimately derive the average current as 9.82 A.
Step-by-step explanation:
The trolley bus question involves finding the average current drawn during its acceleration. We must first find the work done and then the power used since we know the time and efficiency.
First, calculate the kinetic energy (K.E) at the final speed (using K.E = 0.5 * m * v2), where m = 1 × 104 kg and v = 7.6 m/s:
K.E = 0.5 × 1 × 104 kg × (7.6 m/s)2
K.E = 288800 J (Joules)
Since the bus is 40% efficient, the total energy input is greater. Divide the kinetic energy by the efficiency to get the total energy input.
Total energy input = K.E / Efficiency
Total energy input = 288800 J / 0.40 = 722000 J
Power (P) is energy per time (P = Energy / Time). The time taken is 17.1 s, so:
P = 722000 J / 17.1 s = 42222 W or 42.222 kW (since 1 kW = 1000 W)
Since Power (P) is also the product of voltage (V) and current (I), we can write it as P = V × I. Knowing the voltage is 4.3 kV (or 4300 V), we can find the current.
I = P / V = 42222 W / 4300 V = 9.82 A
Therefore, the average current during acceleration is 9.82 A.