A 800. kg car starts from rest and accelerates uniformly to 19.0 m/s in 22.0 s. Assume that air resistance remains constant at 340 N during this time. Find (b) the average power developed by the engine
v=v₀+a•t => a=(v-v₀)/t
m•a=F-F(resist),
F= m•a+F(resist)=
=m• (v-v₀)/t + F(resist)=
=800•(22-0)/22 +340 =…
To find the average power developed by the engine, we can use the formula:
Average Power = Work Done / Time
First, let's calculate the work done by the car. The work done is equal to the force applied multiplied by the distance moved. Since the car is accelerating uniformly, we can use the equation:
Force = Mass * Acceleration
Acceleration = (Final Velocity - Initial Velocity) / Time
Plugging in the given values:
Acceleration = (19.0 m/s - 0 m/s) / 22.0 s
Acceleration = 0.86 m/s²
Force = 800 kg * 0.86 m/s²
Force = 688 N
Next, we need to calculate the distance moved by the car. We can use the equation:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time²
Plugging in the values:
Distance = 0 * 22.0 + (1/2) * 0.86 * (22.0)²
Distance = 10.35 m²
Now, we can calculate the work done:
Work Done = Force * Distance
Work Done = 688 N * 10.35 m²
Work Done = 7111.8 J
Finally, we can calculate the average power:
Average Power = Work Done / Time
Average Power = 7111.8 J / 22.0 s
Average Power = 323.3 W
Therefore, the average power developed by the engine is 323.3 Watts.