The position of a particle moving in a straight line during a 10–second trip is cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip.
The average velocity, vavg, is the average rate of change of a position function s(t) over a time interval [t0, t1].
vavg is defined as
The average velocity of the given position function s(t) during the interval from t0 = 0 s to t1 = 10 seconds is
s(10) = cm
s(0) = cm
The formula for the instantaneous velocity of a particle at time t is found by differentiating the position function s(t).
cm
s'(t) = ·t - cm/s
To find the time when the instantaneous velocity is equal to the average velocity, set s'(t) = vavg and solve for t.
s'(t) = vavg
4·t-2 = 18
t = seconds
(Rounded to one decimal place)