Antiderivatives...A car drives down a road...?
A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is v(t)=2t^(1/2)+4
Find the car's average velocity (in m/s) between t=4 and t=9.
I need to use antiderivatives i know it's s(9)-s(4) and i think that's divided by 9-4 or 5. But I keep getting the wrong answer.. maybe i have the wrong antiderivative..I don't know, please help?
Answers & Comments
Verified answer
Let s = int(4, 9) [ v ] dt
s = [ 2 t^(3 / 2) / (3 / 2) + 4t ] (4, 9)
= [ 4t^(3 / 2) / 3 + 4t ] (4, 9)
= (4 * 27 / 3 + 4 * 9) - (4 * 8 / 3 + 4 * 4)
= 72 - 32 / 3 - 16
= 56 - 32 / 3
= 136 / 3.
The average velocity is:
136 / (3 * 5)
136 / 15.