SOLUTION: A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is
v(t)=2(t)^1/2+4
Find the car's average velocity (in m/s) between t=4 and t=7.
Algebra.Com
Question 466628: A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is
v(t)=2(t)^1/2+4
Find the car's average velocity (in m/s) between t=4 and t=7.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We have to find the average value of the velocity, so we integrate v(t) from t = 4 to t = 7, then divide by 3 seconds. This is similar to finding the total distance traveled, then dividing by 3 s to find the average velocity.
Integrating,
Evaluate it at t = 7, subtract the value at t = 4:
) - (\frac{4}{3}4^{\frac{3}{2}} + 4(3)) = \frac{4}{3} + \frac{28\sqrt{7}}{3})
(meters)
Divide by 3 seconds to obtain
(meters per second)
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