Instantaneous versus average velocity?

• DeltaForce
In summary, the question is asking if the average velocities for different time intervals will differ if the instantaneous velocity remains constant. The average velocity is the change in position over a time interval, while the instantaneous velocity is the velocity at a specific moment.
DeltaForce
Homework Statement
If the instantaneous velocity does not change, will the average velocities for different time intervals differ?
Relevant Equations
avg velocity
instantaneous velocity
I have a hard time understanding what this problem even means. So I can't even begin with it.

DeltaForce said:
Homework Statement: If the instantaneous velocity does not change, will the average velocities for different time intervals differ?
Homework Equations: avg velocity
instantaneous velocity

I have a hard time understanding what this problem even means. So I can't even begin with it.
Maybe I understand. Define for me the average velocity and the instantaneous velocity. How do they differ.?

DeltaForce said:
Homework Statement: If the instantaneous velocity does not change, will the average velocities for different time intervals differ?
Homework Equations: avg velocity
instantaneous velocity

I have a hard time understanding what this problem even means. So I can't even begin with it.
The instantaneous velocity not changing just means the velocity is constant.
If in time interval (t,t+Δt) the position vector changes from ##\vec x## to ##\vec x+\vec{\Delta x}## then the average velocity over that time interval is ##\frac{\vec{\Delta x}}{\Delta t}##.

basically, if ##\frac {d\vec {x}}{dt}## is the same at every moment during the movement, then would you get a different average velocity if you compute it for different time intervals, say between ##t_1## and ##t_2## and between ##t_3## and ##t_4##.

What is the difference between instantaneous and average velocity?

Instantaneous velocity refers to the velocity of an object at a specific moment in time, while average velocity refers to the overall average velocity of an object over a certain period of time.

How is instantaneous velocity calculated?

Instantaneous velocity is calculated by finding the slope of the tangent line at a specific point on a position versus time graph. This can also be calculated by taking the derivative of the position function with respect to time.

What is the significance of instantaneous velocity?

Instantaneous velocity is important because it allows us to analyze an object's motion at a specific point in time, which can provide valuable information about its speed, direction, and acceleration.

How is average velocity calculated?

Average velocity is calculated by dividing the total displacement of an object by the total time taken. This can also be calculated by finding the slope of the line connecting the initial and final positions on a position versus time graph.

When is it more appropriate to use instantaneous velocity versus average velocity?

Instantaneous velocity is more appropriate to use when analyzing an object's motion at a specific moment, such as during a collision or at the peak of a jump. Average velocity is more useful for understanding an object's overall motion over a certain period of time.

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