Visualize a scene featuring a sleek, modern car weighing 1500kg. The car is initially at a standstill, parked on a quiet, paved suburban road. The sun is directly overhead, casting minimal shadow. Suddenly, the car starts to accelerate, reaching a speed of 18m/s within 12 seconds. As it accelerates, hint at a steady resistance force of 400N acting against the car's motion, possibly by showing a wind force or road friction. However, avoid text or numbers. Portray the car's engine working hard, maybe through faint smoke from the exhaust or an energetic glow under the hood.

A car with a mass of 1500kg starts from rest and accelerates to a speed of 18m/s in 12s. Assume that the force of resistance remains constant at 400N during this time. What is the average power developed by the car's engine?

a = (Vf - Vo) / t,

a = (18 - 0) / 12 = 1.5 m/s^2.

Fn = Fap - 400 = 1500 * 1.5,
Fap - 400 = 2250,
Fap = 2650 N. = Force applied.

Vave = (0+18) / 2 = 9 m/s. = Average velocity.

P = Fap * Vave = 2650 * 9 = 23,850 Joules/s = 23,850 Watts.

why did u divide by 2 in the average velocity part the time is 12 seconds not 2?

Why did the car bring a calculator to the party? Because it wanted to calculate its average power, of course! Let's get down to business.

To find the average power developed by the car's engine, we can use the formula:

Power = Work / Time

Now, the work done on the car is equal to the force applied to it multiplied by the distance it travels. We can find the distance by using the equation of motion:

d = (1/2) * a * t^2

where:
d = distance traveled
a = average acceleration
t = time taken

First, we need to find the average acceleration, which can be calculated using the equation:

a = (v - u) / t

where:
v = final velocity
u = initial velocity (which is 0 in this case)

So, let's calculate the average acceleration:

a = (18 m/s - 0 m/s) / 12 s
a = 1.5 m/s^2

Now, let's find the distance traveled:

d = (1/2) * 1.5 m/s^2 * (12 s)^2
d = 108 m

Now that we have the distance traveled, we can calculate the work done on the car:

Work = Force * Distance
Work = (400 N) * (108 m)
Work = 43,200 J

Finally, we can find the average power:

Power = Work / Time
Power = 43,200 J / 12 s
Power = 3,600 W

So, the average power developed by the car's engine is 3,600 Watts. That's quite a powerful engine for a clown car!

To find the average power developed by the car's engine, we need to calculate the work done by the engine and divide it by the time taken.

1. Calculate the net force acting on the car:
The net force is the force of the engine minus the force of resistance.
Net force = Force of the engine - Force of resistance
= Mass * Acceleration - Force of resistance
= 1500 kg * (Change in velocity / Time) - 400 N

2. Calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity
= 18 m/s - 0 m/s
= 18 m/s

3. Calculate the average power:
Average power = (Net force * Change in velocity) / Time
= [(1500 kg * (18 m/s / 12 s)) - 400 N] * 18 m/s / 12 s

Simplifying the expression:
Average power = (20 N/kg * 18 m/s) * 18 m/s / 12 s
= 540 W

Therefore, the average power developed by the car's engine is 540 Watts.

To determine the average power developed by the car's engine, we can use the equation:

Average Power = Work / Time

First, let's find the work done by the car's engine. Since the car starts from rest and accelerates to a speed of 18 m/s, we can use the following equation:

Work = Force * Distance

To find the distance traveled by the car, we can use the equation:

Distance = (Initial Velocity * Time) + (0.5 * Acceleration * Time^2)

Given:
Mass (m) = 1500 kg
Force of Resistance (Fr) = 400 N
Initial Velocity (Vi) = 0 m/s
Final Velocity (Vf) = 18 m/s
Time (t) = 12 s

First, let's find the acceleration of the car. We'll use the equation:

Acceleration = (Vf - Vi) / t

Acceleration = (18 m/s - 0 m/s) / 12 s
Acceleration = 1.5 m/s^2

Now, let's find the distance traveled:

Distance = (Vi * t) + (0.5 * a * t^2)

Distance = (0 m/s * 12 s) + (0.5 * 1.5 m/s^2 * (12 s)^2)
Distance = 0 + 108 m
Distance = 108 m

Next, let's find the work done:

Work = Force * Distance

Work = (Force of Resistance + Force of Engine) * Distance

Since the force of resistance remains constant at 400 N, the force of the engine can be calculated using Newton's second law:

Force = mass * acceleration

Force of Engine = mass * acceleration

Force of Engine = 1500 kg * 1.5 m/s^2
Force of Engine = 2250 N

Work = (400 N + 2250 N) * 108 m
Work = 2650 N * 108 m
Work = 286,200 J

Finally, we can calculate the average power:

Average Power = Work / Time

Average Power = 286,200 J / 12 s
Average Power = 23,850 W

Therefore, the average power developed by the car's engine is 23,850 Watts.