Limits and rate of change

Question

I'm a freshman taking calculus 1 currently studying for finals.
I am reviewing stuff from the beginning of the semester,and I don't remember the proper way to deal with limits like this one.
A ball dropped from a state of rest at time t=0 travels a distance $$s(t)=4.9t^2$$ in 't' seconds. I am told to calculate how far the ball travels between t= [2, 2.5]. I figured this was easy and just plugged in t=.5, but that gave me an answer of 6.0025, and my textbook says it should be 11.025. Can someone please explain why it is 11.025?

Answer 1

At $t=2$ the ball is at position $s(t=2)$. At $t=2.5$, the ball has reached $s(2.5)$. Hence the distance traveled is $s(2.5)-s(2)$.