# Does greater instantaneous velocity mean greater acceleration ?

Two cars are moving in the same direction in parallel lanes along a highway.  At some instant, the instantaneous velocity of car A exceeds the instantaneous velocity of car B.  Does this mean that car A's acceleration is greater than car B's ?  Explain, and use examples.

This is a high school physics question.

I think car A's acceleration is greater than car B's acceleration at the instant car A's instantaneous velocity is greater than car B's instantaneous velocity.  Car A's average acceleration may not be greater than car B's average acceleration.

Am I correct ?
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Commented:
No
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Agree. However they got there, once A is travelling faster than B, that is all it means. It could have taken all day for A to be going faster than B, and it could have taken B 10 seconds to get to its speed, but that is not relevant.

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Commented:
No, because acceleration is the rate of change in velocity, not the velocity itself. If one car is going faster than the other, then yes, the instantaneous velocity may be greater, but the rate of change in velocity may be exactly the same.
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Commented:
Without additional details, no answer can be given. For example, the cars may just be moving at constant speed, i.e. both have zero acceleration. That way, if at time T, the instantaneous velocity of A exceeds that of B, then it will do so at all other times as well.
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Fixer of ProblemsCommented:
Acceleration is only the change in velocity.  If they are both going at a constant velocity and A happens to be going faster, then No, their acceleration is the same, zero, because their individual speeds are not changing.

If car B accelerates to 50 miles per hour then stays at that speed,  car A can wait a while then accelerate to 100 miles per hour and stay at that constant speed and pass car B.  If they are both traveling at their own constant velocities, the acceleration for both is 0.  Zero.
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Commented:
Consider "the instantaneous position of car A exceeds the instantaneous position of car B.  Does this mean that car A's velocity is greater than car B's ? "
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RetiredCommented:
>> the instantaneous velocity of car A exceeds the instantaneous velocity of car B. Does this mean that car A's acceleration is greater than car B's ?  Explain, and use examples

for example
if car A's acceleration is 0 and car B's acceleration is > 0, then, since acceleration is the change in velocity, car B will eventually have a greater instantaneous velocity than car A, if nothing else changes!
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Commented:
Ozo: Consider "the instantaneous position of car A exceeds the instantaneous position of car B.  Does this mean that car A's velocity is greater than car B's ? "

A clear giveaway: "instantaneous". :-)
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Author Commented:
>>   Does this mean that car A's acceleration is greater than car B's

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Author Commented:
>>  Consider "the instantaneous position of car A exceeds the instantaneous position of car B.  Does this mean that car A's velocity is greater than car B's ? "

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Commented:
The question is testing you to see if you can spot the missing information. The fact that one car's instantaneous velocity is greater than another's says almost nothing about the acceleration.

The question is clearly concerned with instantaneous velocity and instantaneous acceleration. As has been mentioned, a car with an acceleration of .1 m/s^2 that has been accelerating for hours will have a much higher velocity than a car with 10 m/s^2 acceleration that just started moving etc etc etc.

Does this mean that car A's acceleration is greater than car B's ?
No. No it does not mean that. You cannot tell anything for sure except that it's going faster now.
Explain, and use examples.
Should be able to pull plenty out of this thread for that.
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