A 1100 kg car accelerates from rest to 27 m/s in 6.0 seconds. Neglecting friction, hat is the average power consumption in horsepower?
a = (V-Vo)/t = (27-0)/6 = 4.5 m/s^2.
d = 0.5a*t^2 = 0.5*4.5*6^2 = 81 m.
Power = F*d/t = Mg*d/t = 1100*9.8*81/6 =
145,530 J/s. = 145,530 Watts.
hp = 145,530/746 = 195.1.
P = 0.5M*V^2/6 = 0.5*1100*27^2/6 = 66,825 J/s = 66,825 W.
hp = 66825/746 = 89.6.
To find the average power consumption of the car, we can use the equation:
Power = (Force × Distance) / Time
First, let's determine the force acting on the car. We can use Newton's second law of motion:
Force = Mass × Acceleration
Given the mass of the car, which is 1100 kg, and the acceleration, which can be calculated using the formula:
Acceleration = Change in Velocity / Time
Change in Velocity = Final Velocity - Initial Velocity
= 27 m/s - 0 m/s
= 27 m/s
Plugging the values into the formula:
Acceleration = 27 m/s / 6.0 s
= 4.5 m/s^2
Now, we can calculate the force acting on the car:
Force = 1100 kg × 4.5 m/s^2
= 4950 N
Next, we need to determine the distance the car traveled. To do this, we can use the average velocity formula:
Average Velocity = (Initial Velocity + Final Velocity) / 2
Plugging in the values:
Average Velocity = (0 m/s + 27 m/s) / 2
= 13.5 m/s
Now, we can use the formula:
Distance = Average Velocity × Time
Distance = 13.5 m/s × 6.0 s
= 81 m
Finally, we can calculate the power consumption in Watts:
Power = (Force × Distance) / Time
= (4950 N × 81 m) / 6.0 s
= 66975 N·m / 6.0 s
= 11162.5 W
To convert the power to horsepower, we can use the conversion factor:
1 horsepower (hp) = 746 Watts
Therefore, the average power consumption of the car is:
Power in horsepower = 11162.5 W / 746
= 14.97 hp (rounded to two decimal places)
So, the average power consumption of the car is approximately 14.97 horsepower.