A 2000kg car accelerates from rest to 36 m/s in 6 seconds. What must the power output of the engine be in order to accomplish this? Express your answer in kilowatts, to three significant figures.
V = Vo + a*T = 30
0 + a*6 = 30
a = 5 m/s^2.
d = 0.5a*T^2 = 0.5*5*6^2 = 90 m.
F = M*a = 2000 * 5 = 10,000 N.
P = F*d/T = 10,000*90/6 = 150,000 J./s = 150,000 W.= 150 kW.
To find the power output of the engine, we can use the equation:
Power = (Force × Distance) / Time
First, we need to calculate the force acting on the car using Newton's second law:
Force = Mass × Acceleration
Given that the mass of the car is 2000 kg and the time taken is 6 seconds, we can find the acceleration:
Acceleration = (Final Velocity - Initial Velocity) / Time
Acceleration = (36 m/s - 0 m/s) / 6 s
Acceleration = 6 m/s^2
Now, we can calculate the force:
Force = Mass × Acceleration
Force = 2000 kg × 6 m/s^2
Force = 12000 N
Next, we need to calculate the distance traveled by the car using the equation of motion:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Distance = 0 m/s × 6 s + (1/2) × 6 m/s^2 × (6 s)^2
Distance = 0 + 1/2 × 6 m/s^2 × 36 s^2
Distance = 0 + 1/2 × 6 m/s^2 × 1296 s^2
Distance = 0 + 1/2 × 7776 m^2/s^2
Distance = 3888 m
Now, we can calculate the power:
Power = (Force × Distance) / Time
Power = (12000 N × 3888 m) / 6 s
Power = 46656000 Nm/s
Power = 46.66 kW
Therefore, the power output of the engine must be approximately 46.66 kW to accelerate the car from rest to 36 m/s in 6 seconds.
To find the power output of the engine, we can use the formula:
Power = (Force) x (Velocity)
However, we need to find the force first. We can use Newton's second law of motion:
Force = mass x acceleration
In this case, the mass of the car is given as 2000 kg, and we can find the acceleration using the formula:
Acceleration = (Change in velocity) / (Time)
Here, the change in velocity is 36 m/s (final velocity) - 0 m/s (initial velocity), which is equal to 36 m/s. The time taken is given as 6 seconds. Substituting these values into the formula, we get:
Acceleration = (36 m/s) / (6 s)
Acceleration = 6 m/s^2
Now we can calculate the force:
Force = (2000 kg) x (6 m/s^2)
Force = 12000 N
Finally, let's find the power:
Power = (Force) x (Velocity)
Since velocity is given as 36 m/s, we can substitute the values:
Power = (12000 N) x (36 m/s)
Power = 432000 N·m/s
To convert this to kilowatts, we can divide by 1000:
Power = 432000 N·m/s / 1000
Power = 432 kW
Therefore, the power output of the engine must be 432 kilowatts to accomplish this acceleration.