Final answer:
To find the applied force produced by the car's engine, we convert the car's velocity to m/s, calculate the acceleration, find the mass from the weight, and use Newton's second law factoring in the friction force. The applied force is approximately 7,000 N.
Step-by-step explanation:
Calculating the Applied Force of a Car Engine
Let's calculate the applied force produced by the engine of the car. To find the applied force, we need to first determine the acceleration of the car and then use Newton's second law of motion.
First, convert the final velocity from km/h to m/s: 83.0 km/h × (1000 m/km) × (1 h/3600 s) = 23.06 m/s.
Next, calculate the acceleration (a) using the formula a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time: a = (23.06 m/s - 0 m/s) / 5.00 s = 4.612 m/s².
Now we use Newton's second law, F_net = ma. However, the net force (F_net) is the applied force (F_app) minus the friction force (F_friction). Therefore, F_app = ma + F_friction.
We know the weight (W) of the car is 12,500 N, which means the mass (m) is W/g, where g is the acceleration due to gravity (9.81 m/s²): m = 12,500 N / 9.81 m/s² = 1274.2 kg.
Using the mass and the acceleration, we can find the applied force: F_app = (1274.2 kg × 4.612 m/s²) + 1350 N. After the calculations, F_app = 5885.11 N + 1350 N = 7235.11 N. The closest answer from the provided options would be (d) 7,000 N.