Solve Velocity Function: Distance in 0-5 Interval

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).
  • #1
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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:
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  • #2
What is a function x(t) whose derivative is v(t)?
 

FAQ: Solve Velocity Function: Distance in 0-5 Interval

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.

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.

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.

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.

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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