Thread: Distance traveled

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) distance traveled.

v(t) = 3t - 5 for 0 less than or equal to t less than or equal to 3

I know how to do part a. The dispalcement is -3/2, but I don't know how to do part b.

I know that the find the distance traveled you need to integrate the absolute value of v(t), and to do that you must split the integral into 2 parts, one where v(t) is less than or equal to 0 and one where v(t) is greater than or equal to zero.

Can someone please explain how you split the integrals? I have no problem integrating 3t - 5, but I don't know what intervals to evaluate it at.

Thanks

Originally Posted by zachb

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) distance traveled.

v(t) = 3t - 5 for 0 less than or equal to t less than or equal to 3

I know how to do part a. The dispalcement is -3/2, but I don't know how to do part b.

The displacement is,

The distance is,


We need to split the integrals for the absolute value.
Now for
This is where we make the seperation.

Okay, I understand how you split the integral now, but I don't understand what you did in the last step.

You started with the definite integral from 0 to 5/3 plus the definite integral from 5/3 to 3, but in the last step you changed it to the definite integral from 0 to 3 plus the definite integral from 5/3 to 3. Why? Is that a mistake, because it doesn't make sense to me.

Originally Posted by zachb

Okay, I understand how you split the integral now, but I don't understand what you did in the last step.

You started with the definite integral from 0 to 5/3 plus the definite integral from 5/3 to 3, but in the last step you changed it to the definite integral from 0 to 3 plus the definite integral from 5/3 to 3. Why? Is that a mistake, because it doesn't make sense to me.

Usually when something does not make sense it is wrong. Judge Judy loves to say that. But to answer your question, yes, I made a mistake and fixed it now.