# Why Does the Lap Time Get Shorter Each Lap?

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This is a multiple choice question where no numbers or values are give; however, I sure it can be deduced through logic.
The question: The mass in the race consists of the mass of the car and the mass of the fuel.
The mass of the fuel decreases as the car completes its journey around the lap.
Why does the lap time decrease with each consecutive lap.

The question never stated that there was friction between the car and the track, so I assumed it wasn't the correct answer.
Therefore, I managed to reduce it down to two solutions, those being
Both the acceleration and deceleration increase
The maximum velocity of the race car increases
I've reasoned that the maximum velocity of the race must increase in order that momentum is conserved. However, some of my classmates have said that the other solution is correct.
So, hopefully someone here can clear things up for me-thanks for any help!

Homework Helper
If the lap time decreased then it went faster with each lap. Why would it go faster for each subsequent lap? Surely the car's power didn't increase.

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Gold Member
Find out what effects the maximum speed.

Clever Penguin
This is a multiple choice question where no numbers or values are give; however, I sure it can be deduced through logic.
The question: The mass in the race consists of the mass of the car and the mass of the fuel.
The mass of the fuel decreases as the car completes its journey around the lap.
Why does the lap time decrease with each consecutive lap.

As the mass of the fuel decreases, the mass of the fuel-car system also decreases. F=ma so, if the force from the engine is the same, it would have a larger acceleration.

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F=ma so, if the force from the engine is the same, it would have a larger velocity.

Larger acceleration.

Clever Penguin
Larger acceleration.

Acceleration

Larger acceleration.
So, the correct answer would be both large acceleration and deceleration or just an increase in maximum velocity?
The question seems that both hold true-but there can only be one.

If the lap time decreased then it went faster with each lap. Why would it go faster for each subsequent lap? Surely the car's power didn't increase.
That's exactly what I'm trying to get my head around, but that's what the question said-it's poorly worded I think.
I though it was just a basic system of decreasing mass type question, therefore momentum needs to be conserved.
But yeah, if power was held constant, then the driving force would decrease which means the acceleration will also need to increase, therefore so will the speed in order to maintain a constant power. The thing is this means that both of them apply.

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So, the correct answer would be both large acceleration and deceleration or just an increase in maximum velocity? The question seems that both hold true-but there can only be one.

Earlier I suggested finding out what limits the maximum velocity. On short straights it might well be the acceleration. On long straights I believe it's air resistance/drag.

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I though it was just a basic system of decreasing mass type question, therefore momentum needs to be conserved.

I'm not sure why you think this is a question about conservation of momentum? A light car accelerates faster but that's not due to conservation of momentum.

Find out what effects the maximum speed.
Earlier I suggested finding out what limits the maximum velocity. On short straights it might well be the acceleration. On long straights I believe it's air resistance/drag.
What would affect the maximum speed other than air resistance? The question is paraphrased slightly as I do not have the paper with me currently, but the question never implied that there was any form of resistance, so I assumed there was none.

I'm not sure why you think this is a question about conservation of momentum? A light car accelerates faster but that's not due to conservation of momentum.
OK, so would the deceleration decrease also?
And why would momentum not be conserved if the system's mass decreases and the fuel move in an opposite direction to that of the car with some velocity, so the car's velocity will also need to increase to negate this change?

OK, so would the deceleration decrease also?
And why would momentum not be conserved if the system's mass decreases and the fuel move in an opposite direction to that of the car with some velocity, so the car's velocity will also need to increase to negate this change?
Sorry, I meant to say would the deceleration increase also

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OK, so would the deceleration decrease also?

What do you think? A car with less mass has less inertia so is it easier or harder to stop?.

And why would momentum not be conserved if the system's mass decreases and the fuel move in an opposite direction to that of the car with some velocity, so the car's velocity will also need to increase to negate this change?

Only a rocket car pushes itself along by throwing fuel out of the back. All other cars work by pushing the ground backwards. Momentum is conserved but you have to take into account the effect the car has on the rotation of the planet. We could discuss this but conservation of momentum isn't relevant to this problem.

NihalRi
I definitely agree that the final velocity increases, like you said because momentum in conserved. Intuitively the acceleration would also increase, but why would it decrease? And if acceleration decreases and increases why don't the effects cancel out? That one just doesn't make any sense to me, hopefully I'm not missing anything important.

Clever Penguin
What do you think? A car with less mass has less inertia so is it easier or harder to stop?.

My thoughts are that it is easier to stop, since a smaller force is required to produce the same acceleration/deceleration

CWatters
What do you think? A car with less mass has less inertia so is it easier or harder to stop?.

Only a rocket car pushes itself along by throwing fuel out of the back. All other cars work by pushing the ground backwards. Momentum is conserved but you have to take into account the effect the car has on the rotation of the planet. We could discuss this but conservation of momentum isn't relevant to this problem.
So
I definitely agree that the final velocity increases, like you said because momentum in conserved. Intuitively the acceleration would also increase, but why would it decrease? And if acceleration decreases and increases why don't the effects cancel out? That one just doesn't make any sense to me, hopefully I'm not missing anything important.
Yeah, it doesn't make sense to me. The thing I think is missing from a lot of these answers is that would both the acceleration and deceleration decrease.

So

Yeah, it doesn't make sense to me. The thing I think is missing from a lot of these answers is that would both the acceleration and deceleration decrease.
Sorry, would both increase.

What do you think? A car with less mass has less inertia so is it easier or harder to stop?.

Only a rocket car pushes itself along by throwing fuel out of the back. All other cars work by pushing the ground backwards. Momentum is conserved but you have to take into account the effect the car has on the rotation of the planet. We could discuss this but conservation of momentum isn't relevant to this problem.
Yeah, my understanding of physics is only elementary at this point, I am a first year A-level student, this seems more like undergraduate level stuff. Regardless, it seems to me that this question in unanswerable as both potential answers apply to the situation.

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Ok so I agree. A lighter car accelerates and decelerates faster than a heavy one.

More in a moment.

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Reminder, the two options were..

Both the acceleration and deceleration increase
The maximum velocity of the race car increases

We agree that the first option is a valid answer. Cars that accelerate and decelerate faster spend more time going fast so have a shorter lap time.

The second option is slightly ambiguous. Does it mean the maximum possible velocity (eg on an infinitely long straight) or the maximum velocity between bends on a real world racing track? Let's consider both possibilities...

The maximum velocity on an infinitely long straight is usually limited by air resistance or possibly the cars gearing and rev limiter. Either way it's not usually affected by the cars weight (or at least not directly).

On a real world track with short straights between bends the maximum velocity is dependant on how fast the car can accelerate and decelerate. Basically they go around a bend then accelerate flat out until they run out of space and have to start slowing down for the next bend.

So even though you can argue the question is ambiguous, in both cases it's not as valid an answer as the one about acceleration and deceleration.

Clever Penguin
NihalRi
Hold on, perhaps momentum isn't conserved because energy is being provided by the fuel. We all agree that power is conserved though, thus so is the force provided by the engine.
F = ma =Δp/Δt
So with time decreasing the formula above suggests the change in momentum increases.

Ah, that definitely clear
Reminder, the two options were..

We agree that the first option is a valid answer. Cars that accelerate and decelerate faster spend more time going fast so have a shorter lap time.

The second option is slightly ambiguous. Does it mean the maximum possible velocity (eg on an infinitely long straight) or the maximum velocity between bends on a real world racing track? Let's consider both possibilities...

The maximum velocity on an infinitely long straight is usually limited by air resistance or possibly the cars gearing and rev limiter. Either way it's not usually affected by the cars weight (or at least not directly).

On a real world track with short straights between bends the maximum velocity is dependant on how fast the car can accelerate and decelerate. Basically they go around a bend then accelerate flat out until they run out of space and have to start slowing down for the next bend.

So even though you can argue the question is ambiguous, in both cases it's not as valid an answer as the one about acceleration and deceleration.
That definitely clears things up, it is a pretty strange question and poorly worded; annoyingly, it was also worth only one mark.
But yeah, that makes perfect sense thanks for all your help!

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Gold Member
Hold on, perhaps momentum isn't conserved because energy is being provided by the fuel. We all agree that power is conserved though, thus so is the force provided by the engine.

Power = force * velocity

If the power is constant then, as the car accelerates and the velocity increases the force reduces. So force is not constant.

Clever Penguin
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Just to make one point clear -- Conservation of momentum can only be used when no external forces are being applied. There is no conservation of momentum when the engine, brakes, or turning are applying forces on the car (by way of tire force on the ground). To use the conservation law, the Earth would have to be included in the system. That would make those tire forces internal to the system.

Clever Penguin
NihalRi
acceleration and deceleration.
Ok, so a lighter car
Power = force * velocity

If the power is constant then, as the car accelerates and the velocity increases the force reduces. So force is not constant.
You're right of course, I deserve a slap on the face for that one lol