a car accelerates uniformly from rest to 29 m/s in 12s along a level of road. ignoring friction, determine the average power (hp) required to accelerate the car if the weight of the car is 1.2 x 10^4 N.
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To find the average power required to accelerate the car, we can use the formula for average power:
Average Power = Work Done/Time
The work done can be found using the formula for work:
Work Done = Force x Distance
In this case, the force acting on the car is its weight, and the distance is the displacement of the car. Since the car starts from rest and accelerates uniformly, we can use the equations of motion to find the displacement.
The equation that relates the final velocity (v), initial velocity (u), acceleration (a), and time (t) is:
v = u + at
In this case, the initial velocity (u) is 0 m/s, the final velocity (v) is 29 m/s, and the time (t) is 12 s. We can rearrange the equation to solve for acceleration (a):
a = (v - u) / t
Substituting the given values:
a = (29 m/s - 0 m/s) / 12 s
a = 29 m/s / 12 s
a ≈ 2.42 m/s²
Now, we can find the displacement using the equation:
s = ut + (1/2)at²
Since the initial velocity (u) is 0 m/s, the equation simplifies to:
s = (1/2)at²
Substituting the values:
s = (1/2) * 2.42 m/s² * (12 s)²
s = (1/2) * 2.42 m/s² * 144 s²
s ≈ 174.912 m
Now that we have the displacement and the weight of the car, we can calculate the work done:
Work Done = Force x Distance
Work Done = Weight x Displacement
Substituting the given values:
Work Done = (1.2 x 10^4 N) x 174.912 m
Work Done ≈ 2098.94 J
Now, we can calculate the average power:
Average Power = Work Done / Time
Substituting the given time:
Average Power = 2098.94 J / 12 s
However, we need to convert the average power from joules/second (watts) to horsepower (hp). 1 horsepower (hp) is approximately equal to 746 watts.
So, the average power in horsepower (hp) is:
Average Power = (2098.94 J / 12 s) / 746 W/hp
Average Power ≈ 0.282 hp
Therefore, the average power required to accelerate the car is approximately 0.282 horsepower.
To determine the average power required to accelerate the car, we need to use the formula:
Average power = work done / time
First, we need to calculate the work done. In this case, work done is equal to the change in kinetic energy of the car.
The formula for kinetic energy is:
Kinetic energy = (1/2) * mass * velocity^2
Since we are given the weight of the car (1.2 x 10^4 N) and acceleration (which we can calculate from the given information), we can find the mass of the car using the formula:
Weight = mass * acceleration due to gravity
Rearranging the equation to solve for mass, we have:
mass = weight / acceleration due to gravity
Next, we can calculate the acceleration using the formula for uniformly accelerated motion:
acceleration = (final velocity - initial velocity) / time
Plug in the given values:
initial velocity = 0 m/s
final velocity = 29 m/s
time = 12 s
Using the equation above, we can find the acceleration.
Once we have the mass and acceleration, we can calculate the work done by substituting the values in the formula for kinetic energy.
Finally, divide the work done by the time to get the average power. Recall that 1 horsepower is equal to 746 watts, so you can convert the result to horsepower if necessary.