a car with a mass of 1.50 x 10^3 kg starts from rest and acceleration to a speed of 18.0 m/s in 12.0 s. Assume that the force of resistance remains constant at 400.0 N during this time. What is the average power developed by the cars engine
M*g = 1500 * 9.8 = 14,700 N. = Wt. of car. = Normal(Fn).
V = Vo + a*t = 18.
0 + a*12 = 18, a = 1.5 m/s^2.
d = 0.5a*t^2 = 0.75*12^2 = 108 m.
Fr = 400 N.
Fe-Fr = M*a.
Fe = M*a+Fr = 2250 + 400 = 2650 N. = Force of engine.
P = Fe*d/t = 2650 * 108/12 = 23,850 J/s = 23,850 Watts.
Well, it sounds like this car really had to put the pedal to the metal! Let's calculate the average power developed by its engine.
To find the average power, we can use the formula: average power = work done/time. In this case, the work done is equal to the force applied multiplied by the distance traveled.
First, let's calculate the distance traveled. We can use the formula: distance = initial velocity * time + (1/2) * acceleration * time^2.
Given:
Initial velocity (u) = 0 (since the car starts from rest)
Final velocity (v) = 18.0 m/s
Time (t) = 12.0 s
Acceleration (a) = (v - u)/t = (18.0 - 0)/12.0
Now let's calculate the distance:
distance = 0 * 12.0 + (1/2) * [(18.0 - 0)/12.0] * (12.0)^2
We find the distance to be 72.0 meters.
Now, let's calculate the work done. The force applied is 400.0 N, and the distance traveled is 72.0 meters.
work done = force * distance = 400.0 N * 72.0 m
Finally, we can calculate the average power:
average power = work done / time = (400.0 N * 72.0 m) / 12.0 s
And the answer is... *drum roll* 2400.0 Watts!
So, the average power developed by the car's engine is 2400.0 Watts. Keep in mind, though, that this is just the average power, not the peak power. I hope my calculations didn't drive you crazy!
To find the average power developed by the car's engine, we can use the formula for power:
Average Power = (Work done) / (Time taken)
First, we need to find the work done. The work done is the product of the force and the distance traveled. Since the car starts from rest and accelerates to a final velocity of 18.0 m/s, we can use the equation of motion:
v = u + at,
where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time taken.
Using this equation, we can rearrange it to solve for the acceleration, a:
a = (v - u) / t.
Plugging in the values:
a = (18.0 m/s - 0) / 12.0 s = 1.50 m/s^2.
Now, we can find the force required to accelerate the car using Newton's second law of motion:
F = ma,
where F is the force, m is the mass of the car, and a is the acceleration.
Plugging in the values:
F = (1.50 x 10^3 kg) * (1.50 m/s^2) = 2250 N.
Now we need to find the net force acting on the car. It is given that the force of resistance remains constant at 400.0 N during this time. So, the net force is:
Net Force = Force of acceleration - Force of resistance,
Net Force = 2250 N - 400.0 N = 1850 N.
Next, we need to find the distance traveled by the car. We can use the equation of motion:
s = ut + (1/2)at^2,
where s is the distance, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time taken.
Plugging in the values:
s = (0) * (12.0 s) + (1/2) * (1.50 m/s^2) * (12.0 s)^2 = 108.0 m.
Now, we can find the work done by the net force:
Work = Force * Distance,
Work = 1850 N * 108.0 m = 199,800 J (Joules).
Finally, we can calculate the average power developed by the car's engine:
Average Power = Work / Time,
Average Power = 199,800 J / 12.0 s ≈ 16,650 W (Watts).
Therefore, the average power developed by the car's engine is approximately 16,650 Watts.
To find the average power developed by the car's engine, we need to calculate the net work done on the car and divide it by the time taken.
The net work done on an object is given by the equation:
Work = Force × Distance
In this case, the force acting on the car is the sum of the force applied by the engine and the force of resistance:
Force = Force by engine - Force of resistance
The distance traveled by the car can be calculated using the equation of motion:
Distance = (Initial velocity × Time) + (1/2 × Acceleration × Time^2)
Let's calculate the force, distance, and work:
Given:
Mass of the car (m) = 1.50 × 10^3 kg
Force of resistance (Fresistance) = 400.0 N
Initial velocity (u) = 0 m/s
Final velocity (v) = 18.0 m/s
Time (t) = 12.0 s
Acceleration (a) can be calculated using the equation of motion:
v = u + (a × t)
Rearranging the equation, we get:
a = (v - u) / t
a = (18.0 m/s - 0 m/s) / 12.0 s
a = 18.0 m/s / 12.0 s
a = 1.5 m/s^2
Now, let's calculate the distance traveled by the car:
Distance = (0 m/s × 12.0 s) + (1/2 × 1.5 m/s^2 × (12.0 s)^2)
Distance = 0 m + (1/2 × 1.5 m/s^2 × 144.0 s^2)
Distance = 108.0 m
Now we can calculate the force applied by the engine:
Force = Force by engine - Force of resistance
Force by engine = Force + Force of resistance
Force by engine = m × a + Fresistance
Force by engine = (1.50 × 10^3 kg) × (1.5 m/s^2) + 400.0 N
Force by engine = 2250 N + 400.0 N
Force by engine = 2650 N
Finally, we can calculate the net work done on the car:
Work = Force × Distance
Work = (2650 N) × (108.0 m)
Work = 286,200 J
Now, we can calculate the average power developed by the car's engine:
Average Power = Work / Time
Average Power = 286,200 J / 12.0 s
Average Power = 23,850 W
Therefore, the average power developed by the car's engine is 23,850 Watts (W).