Find the average velocity of the particle over the time interval [1,1+h] After t seconds the displacement, s(t), of a particle moving rightwards along the t-axis is given (in feet) by s(t) = (1/4)t^3

Expert Answers
lfryerda eNotes educator| Certified Educator

The average velocity of the particle is given by the difference in displacement divided by the difference in times.  This means that we calculate this as:

`v={s(1+h)-s(1)}/{1+h-1}`   simplify

`={1/4(1+h)^3-1/4(1)}/{h}`   expand numerator and factor 1/4

`={1+3h+3h^2+h^3-1}/{4h}`

`={3h+3h^2+h^3}/{4h}`    cancel common factor of h

`=1/4(3+3h+h^2)`

The average velocity is `v=1/4(3+3h+h^2)` .