Derivative as a rate if change - is this correct?

[donjt81]

I did this problem but wasnt sure if I did it right. Can anyone check it and see if my approach is correct?

here is the question:
The position of a moving body is given by s = f(t) = t^2 + 24t -1 for 0 <= t <= 8 where s is measured in meters and t in sec. Find the body's displacement for the time interval t = 3 to the time when the velocity is 34 m/s.

here is what i did:
s' = velocity = 2t + 24
34 = 2t + 24
t = 5

so the time interval is 3 <= t <= 5
t + delta t = 5
t = 3

displacement = f(t + delta t) - f(t)
= (5^2 + 24*5 - 1) - (3^2 + 24*3 - 1)
= 144 - 80
= 64 meters

I am wondering if this is correct. I wonder why they put the interval 0 <= t <= 8 ... maybe to throw us off. i don't know...

thanks in advance

 

[courtrigrad]

yeah that's correct.

 

[donjt81]

thanks a lot!