Question

At a given instant in time, two cars are traveling at different velocities, one twice as large as the other. Based on this information, is it possible to say which of these two cars has the larger acceleration at this instant in time?

Answer 1

Answer: No, is not possible.

Explanation:

We have two cars traveling at different velocities, one with velocity v and other with velocity 2*v

We want to know of it is possible to say which of these two cars has the larger acceleration at this instant of time.

Acceleration is the rate of change of the velocity, for example, if acceleration = 0, the velocity does not change.

Notice that knowing only the velocity at a given instant of time, we do not have any way of knowing the acceleration of each car.

Such that acceleration is given by the second Newton's equation:

F = m*a

force equals mass times acceleration.

We do not know any of these quantities for the cars, so we can not say anything about the accelerations.

We also could know the average acceleration if we know the change in velocity over an interval of time, such that:

Av acceleration = (change in velocity)/(interval of time)

But here we do not have a change in velocity, so again, we can't say anything about the acceleration.