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

1 Answer

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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)` .

Sources: