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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 dont know...

thanks in advance