Motion equation problem -- Car accelerating with a constant power engine

In summary, the conversation discusses the speaker's attempts to solve a problem using two different methods, resulting in different outcomes. The second method is deemed correct due to the presence of non-constant acceleration, in contrast to the first method which utilizes SUVAT equations that only apply to constant acceleration. The differential equation expressing constant power is also mentioned.
  • #1
Weber_per_metermeter
2
1
Homework Statement
In horizontal straight line path, there's a car, weighing 600kg, fully powered with P=25kW, that is constant during motion. Car is starting from rest state (v0=0). What is the speed intensity after s=125m of driving? Enviromental resistance and friction are negligible.
Relevant Equations
P=F*v=m*a*v
v^2=v0^2+2as
So I tried to solve this in two methods, but I keep getting different results, and I don't know why.
IMG-20201015-WA0010.jpg
 
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  • #2
It's hard to read, but you seem to be using SUVAT equations. Those only apply when acceleration is constant. Here, power is constant.
Write the differential equation that expresses that.

Edit: managed to get a clearer image of your work, and I see you did use the right method in the second attempt, as @TSny notes.
 
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  • #3
Your first method is not correct due to the reasons @haruspex mentioned. Your second method looks OK to me.
 
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  • #4
Thank you for your answer. Now that you mentioned it, of course its due to non constant acceleration :D
Great work!
 
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1. What is the equation for calculating the acceleration of a car with a constant power engine?

The equation for calculating the acceleration of a car with a constant power engine is a = P/(m*v), where a is the acceleration, P is the power of the engine, m is the mass of the car, and v is the velocity.

2. How does the power of the engine affect the acceleration of a car?

The power of the engine directly affects the acceleration of a car. The higher the power, the faster the car will accelerate. This is because a more powerful engine can produce more force to overcome the car's mass and increase its velocity.

3. Can the acceleration of a car with a constant power engine be increased?

Yes, the acceleration of a car with a constant power engine can be increased by reducing the car's mass or increasing its velocity. This is because the acceleration is inversely proportional to the mass and directly proportional to the velocity.

4. How does the mass of the car affect its acceleration?

The mass of the car has an inverse relationship with its acceleration. This means that the lighter the car, the faster it will accelerate with the same amount of power from the engine. This is because a lighter car requires less force to move and therefore can reach higher velocities more quickly.

5. How can the acceleration of a car be calculated if the power and velocity are known?

The acceleration of a car can be calculated using the equation a = P/(m*v), where P is the power of the engine and v is the velocity of the car. Simply plug in the values and solve for a to find the acceleration in m/s².

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