- #1
christian0710
- 409
- 9
Hi if i have a function that relates time and distance travelled, is this correctly understood: (please tell me what is correct and what is wrong - it would help me understand)
The function is
f(t)=16(t^2)
1. f(4) = 256 This tells me that at the END of 4 seconds (or is it at the beginning?) i traveled a total distance of 256 ft so the number 256 has the units feet
2. d(f(5))/dt = 256 tells me that at 5 seconds my instantaneous speed is 256 feet per seconds, so the units are feet/seconds
My final question is this: How can an object have an instantaneous speed of 256 ft/seconds at 5 seconds, if the object has only traveled 256 feet by the END of 4 seconds (which is close to 5 seconds)??
The idea that f(4) means "At the end of 4 seconds" is something i got from "Calculus an intuitive and physical approach" says on page 24 at the top.
The function is
f(t)=16(t^2)
1. f(4) = 256 This tells me that at the END of 4 seconds (or is it at the beginning?) i traveled a total distance of 256 ft so the number 256 has the units feet
2. d(f(5))/dt = 256 tells me that at 5 seconds my instantaneous speed is 256 feet per seconds, so the units are feet/seconds
My final question is this: How can an object have an instantaneous speed of 256 ft/seconds at 5 seconds, if the object has only traveled 256 feet by the END of 4 seconds (which is close to 5 seconds)??
The idea that f(4) means "At the end of 4 seconds" is something i got from "Calculus an intuitive and physical approach" says on page 24 at the top.