Question

Distance travelled by a car in feet is given by: `t^3-9t^2+24t+5`, how do you determine the average velocity over the interval (1,2)?

Answer 1

`4` feet/time unit (or less) in some unknown direction.

Explanation:

If `f(t)=t^3-9t^2+24t+5` is the distance (in feet) traveled after `t` (?seconds):

`f(1)=1^3-9(1^1)+24(1)+5 = 21`

`f(2)=2^3-9(2^2)+24(2)+5 = 8-36+48+5 = 25`

Time interval length (`Deltat`) `= 2-1=1` (time unit; maybe seconds)

Average speed = ((f(2)-f(1))/(2-1) = 4 # feet/(?second?)

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Note that velocity should have a direction component.

If the car is traveling in a straight line its velocity will be 4 feet/(time unit) in the direction of travel;

if it is not going in a straight line its velocity will be less than 4 feet/time unit in a direction which can not be determined from the given information.