Kinetics with Veloctiy/Acceleration Problem

• azn1x6flame
In summary, the problem asks to find the distance traveled by a particle given its velocity function. The attempt at a solution involves finding the anti-derivative of the velocity function and using the integral to calculate the distance. However, the calculated distance is not matching the answer provided in the book.
azn1x6flame
Hello, I need help on this following problem on velocity/acceleration

1. 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 interval2. Homework Equations

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

3. The Attempt at a Solution

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

But it isn't correct, can someone help me with this problem?

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

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

That's the velocity of the particle at t=5. It's not the total distance travelled.

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?

The anti-derivative is just the integral. Do you know how to find the integral of a polynomial?

ideasrule said:
That's the velocity of the particle at t=5. It's not the total distance travelled.
The anti-derivative is just the integral. Do you know how to find the integral of a polynomial?

Yes. This is what I have so far and it's coming up negative:

3/2*t^2-11*t from 0 to 5, so 3/2*25-55 -0 = 125/2-55=-17.5

Whereas the answer book is showing: 137/6

So for some reason, my answer isn't totaling correctly

1. What is kinetics in relation to velocity/acceleration?

Kinetics is a branch of physics that studies the motion of objects and their interactions with forces. In relation to velocity and acceleration, kinetics focuses on how these quantities change over time and how they are affected by external forces.

2. How is velocity related to acceleration?

Velocity and acceleration are related through the derivative of position. Velocity is the rate of change of position, while acceleration is the rate of change of velocity. In other words, acceleration is the change in velocity over time.

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

Average velocity/acceleration is calculated over a specific time interval, while instantaneous velocity/acceleration is the velocity/acceleration at a specific moment in time. Average velocity/acceleration gives an overall picture of an object's motion, while instantaneous velocity/acceleration gives a more detailed and precise understanding.

4. How do you calculate velocity/acceleration from a given position vs. time graph?

Velocity can be calculated by finding the slope of the tangent line to the position vs. time graph at a specific point. Acceleration can be calculated by finding the slope of the tangent line to the velocity vs. time graph at a specific point.

5. What are some real-world applications of kinetics with velocity/acceleration?

Kinetics with velocity/acceleration has many practical applications, such as in the design of roller coasters, cars, and airplanes. It is also used in sports, such as calculating the speed and acceleration of a baseball pitch or a runner on a track. Kinetics is also important in understanding the movement and behavior of particles in chemistry and in studying the motion of planets and other celestial bodies in astronomy.

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