If a car's velocity is given by v(t) = t + 25 miles per hour, how far has the car traveled between the times t = 1 hour and t = 3 hours

2. Originally Posted by bobby77
If a car's velocity is given by v(t) = t + 25 miles per hour, how far has the car traveled between the times t = 1 hour and t = 3 hours
Not exactly sure what you are asking.
v(1) = 26 mph
v(3) = 28 mph
So the car is moving between 26 and 28 mph during the times t = 1 hr and t = 3 hr.

Was that what you were looking for? The only other thing I can think of is that you are looking for an average speed which would be $\frac{26+28}{2}=27 \, mph$ since v is a linear function of t.

-Dan

3. $s=\int|v|dt$, but since the velocity function isn't negative on your interval you can drop the absolute value brackets. So the total distance traveled is $\int_{1}^{3}t+25dt=54miles$

4. (Sigh). I hate it when I read the question wrong!

-Dan

5. It happens to the best of us. I wish I could say that was the reason I can't answer a question correctly.