Calculus

The position (feet traveled) of a car is given by the equation s(t)=(1/4)t^2+1
find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds
t=0
t=2.5
t=5
t=10
Never

I think it's either t=5 or t=2.5?
The end points are (0,1) and (10,26) so the average speed would be 2.5 right? The derivative is x/2 so would the average speed just be 2.5 or would you use the derivative (5/2=2.5) and then the answer would be 5?

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  1. the speed according to your function is t/2, not x/2
    so you want
    t/2 = 2.5
    t = 5 <------ that is the time when the two speeds are the same
    and the instantaneous speed at that time is t/2 = 5/2 or 2.5 ft/s

    But it asked for the time when they were equal and that is 5 seconds

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  2. Sorry, to make it easier in my work I changed t to x. Thank you so much for your help!

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  3. Also, what could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor? Would it be meters per radian?
    (Square millimeters per millimeter
    Millimeters per centimeter
    Meters per second
    Gallons per hour
    Or meters per radian)

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