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?

4 answers

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
Sorry, to make it easier in my work I changed t to x. Thank you so much for your help!
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)
Square millimeters per millimeter