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
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.