A car with a mass of 1264 kg is coasting in neutral on a straight,level road. It slows down, and its speed as a function of time is given by the equation:
Constant Value Units
a 26.8 m/s
b 0.310 m/s2
c 2.10·10-3 m/s2
At a time of 36.0 s the speed, as given by the above equation, is 18.36 m/s. Calculate the power which the engine must deliver (to compensate for air resistance and rolling resistance) in order to maintain that speed.
the equation:
v(t) = a − bt + ct2
To calculate the power which the engine must deliver to maintain a certain speed, we need to consider the total force acting on the car. The power can be calculated using the equation:
Power = Force x Speed
First, let's calculate the force acting on the car. The total force can be broken down into two components: the force due to air resistance (drag force) and the force due to rolling resistance.
1. Drag Force:
The drag force acting on the car can be calculated using the equation:
Drag Force = 0.5 x density x coefficient of drag x frontal area x speed^2
In this equation, we need to know the density of air, the coefficient of drag, frontal area, and speed. Unfortunately, the given information does not provide these values. So, we cannot calculate the exact drag force in this case.
2. Rolling Resistance:
The rolling resistance force can be calculated using the equation:
Rolling Resistance Force = coefficient of rolling resistance x car weight
To calculate the rolling resistance force, we need to determine the weight of the car. Weight can be calculated using the equation:
Weight = mass x acceleration due to gravity
Given the mass of the car as 1264 kg, and the acceleration due to gravity as approximately 9.8 m/s^2, we can calculate the weight of the car.
Weight = 1264 kg x 9.8 m/s^2 = 12387.2 N
Now that we have the weight, we can calculate the rolling resistance force. Let's assume a coefficient of rolling resistance (crr) value of 0.01, although the actual value may differ.
Rolling Resistance Force = 0.01 x 12387.2 N = 123.872 N
Now, we can calculate the total force acting on the car by summing the drag force and the rolling resistance force.
Total Force = Drag Force + Rolling Resistance Force
Since we don't have the exact value for the drag force, we cannot calculate the total force accurately. However, we can approximate the total force by assuming a reasonable value for the drag force, based on typical car performance. Let's assume a drag force of 200 N.
Total Force = 200 N + 123.872 N = 323.872 N
Finally, we can calculate the power required to maintain the given speed of 18.36 m/s.
Power = Force x Speed = 323.872 N x 18.36 m/s = 5941.46 watts
Therefore, the engine must deliver approximately 5941.46 watts (or 5.94 kilowatts) of power to maintain a speed of 18.36 m/s, considering drag force and rolling resistance.