Calculating power without distance?

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In summary, the conversation revolves around a homework problem that asks for the kinetic energy of a vehicle moving at a certain speed and the average power developed if it accelerated to that speed in 20 seconds. The formula for power involves distance, which is not given in the problem, leading to confusion and questioning. Ultimately, it is determined that the average kinetic energy can be calculated and used to find the average power.
  • #1
fattydq
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So here's my homework problem:

Calculate KE of a 1500 kg vehicle moving at 30 m/2. Which I did, and got 675000 joules, using the standard KE formula.

But then it asks, if the vehicle accelerated to this speed in 20 seconds, what average power was developed?

Any formula for power involves a distance, which is not given here at all. Can someone help me out? Is it a trick question?
 
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  • #2
fattydq said:
So here's my homework problem:

Calculate KE of a 1500 kg vehicle moving at 30 m/2. Which I did, and got 675000 joules, using the standard KE formula.

But then it asks, if the vehicle accelerated to this speed in 20 seconds, what average power was developed?

Any formula for power involves a distance, which is not given here at all. Can someone help me out? Is it a trick question?

If it acquires its energy in some amount of time, that implies an average power level input during that time interval...
 
  • #3
As long as the acceleration is constant, the average velocity is the average of the starting and ending velocities. You can use that to find the average kinetic energy.

And I am surprised to hear that "Any formula for power involves a distance". I was under the impression that "power" was "rate of change of energy over time".

(You could, of course, calculate the distance moved at a constant acceleration in a given time. For constant acceleration, a, and time, t, the velocity is at. You can use that to find a from the information given. The distance moved is [itex](1/2)at^2[/itex].)
 
  • #4
Well the reason I thought I needed a distance was because the formula for power is the change in work over the change in time. SOOOO the formula for work is force times DISTANCE. So I don't understand how can I calculate power if I can't find work.
 
  • #5
fattydq said:
Well the reason I thought I needed a distance was because the formula for power is the change in work over the change in time. SOOOO the formula for work is force times DISTANCE. So I don't understand how can I calculate power if I can't find work.

It's not change in work, it's amount of work (or energy) in some amount of time.
 
  • #6
berkeman said:
It's not change in work, it's amount of work (or energy) in some amount of time.

So I just divide the numerical answer for kinetic energy by 20?
 
  • #7
fattydq said:
So I just divide the numerical answer for kinetic energy by 20?

I believe that is correct.
 

1. How is power calculated without distance?

In order to calculate power without distance, you would need to know the amount of force applied and the time it takes to apply that force. The formula for calculating power is power = force * velocity. In this case, velocity is the distance traveled over time, which can be simplified to velocity = distance / time. By substituting this into the power formula, we get power = force * (distance / time). Therefore, power can be calculated without distance by using force and time instead of distance and time.

2. Why is power without distance important in science?

Power without distance is important in science because it allows us to understand the amount of work being done without having to consider the distance traveled. This is especially useful in situations where the distance traveled is not relevant or is difficult to measure. Additionally, it helps us to compare the efficiency of different processes or machines by looking at the amount of power they produce without being influenced by the distance over which the power is applied.

3. Can power be calculated without knowing the distance?

Yes, power can be calculated without knowing the distance. As mentioned before, power can be calculated using the formula power = force * (distance / time). If we rearrange this formula to solve for distance, we get distance = (power * time) / force. Therefore, if we know the power, time, and force, we can calculate the distance. However, in situations where distance is not relevant or difficult to measure, we can still calculate power without knowing the distance.

4. What are some real-life examples of calculating power without distance?

There are many real-life examples of calculating power without distance. For example, when measuring the power output of an engine, we do not need to consider the distance traveled by the vehicle, but rather focus on the force and time it takes for the engine to produce that power. Another example is a weightlifting competition, where the power of an athlete is determined by the amount of weight they can lift within a certain amount of time, without considering the distance the weight is lifted.

5. How does power without distance relate to the concept of work?

Power without distance and the concept of work are closely related. Work is defined as the amount of force applied over a certain distance. Therefore, power, which is the amount of work done per unit of time, can be calculated without distance by using force and time instead. This allows us to understand the rate at which work is being done without being influenced by the distance traveled.

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