# Solve Velocity Function: Distance in 0-5 Interval

• azn1x6flame
In summary, the conversation is about finding the distance traveled by a particle with a given velocity function over a given time interval. The attempt at solving the problem and the need for finding the anti-derivative of the velocity function is mentioned. The person ultimately figures out the answer and thanks anyone who may have helped. They also ask for a function x(t) whose derivative is v(t).
azn1x6flame
Hello, I need help on this following problem on velocity

## Homework Statement

The velocity function (in meters per second) is given for a particle moving along a line.

v(t)=3t-11, 0 (greater than or equal to) t (greater than or equal to) 5

Find the distance (in meters) traveled by the particle during the given time interval

## Homework Equations

v(t)=3t-11, 0 (greater than or equal to) t (greater than or equal to) 5

## The Attempt at a Solution

I tried the following:
3(5)-11=4

But it isn't correct.

I know I have to find the anti-derivative of v(t).

How would I find t? Do I have to do the derivative of v(t) to find acceleration? Would that help me do this problem?

Can someone help me with this problem?

Thanks

Edit: I figured out this answer. Thanks.

Last edited:
What is a function x(t) whose derivative is v(t)?

## 1. What is the formula for velocity?

The formula for velocity is v = Δx/Δt, where v is velocity, Δx is the change in position, and Δt is the change in time.

## 2. How do you solve for velocity using the distance function?

To find the velocity using the distance function, you can use the formula v = dx/dt, where v is velocity, dx is the change in distance, and dt is the change in time. This formula calculates the instantaneous velocity at a specific time point within the given interval.

## 3. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity at a specific moment in time. Average velocity gives an overall picture of the object's motion, while instantaneous velocity shows how fast the object is moving at that particular time.

## 4. How do you interpret a velocity vs. time graph?

A velocity vs. time graph shows the velocity of an object over a specific time interval. The slope of the graph represents the acceleration of the object, while the area under the curve represents the displacement. A positive slope indicates a positive acceleration, meaning the object is speeding up, while a negative slope indicates a negative acceleration, meaning the object is slowing down.

## 5. Can you solve for velocity if only given the distance function over a specific interval?

Yes, you can solve for velocity using the distance function over a specific interval. You can use the formula v = Δx/Δt or v = dx/dt to find the average or instantaneous velocity, respectively. However, if the distance function is not given as a continuous function, it may be more difficult to accurately calculate the velocity.

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