The position of a particle moving in a straight line during a $t–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 = $t seconds is
where s($t) = ktPlo8x7WLY= cm
and s(0) = fb59X/mhrUU= cm.
vavg = /14Ao413H505SJO7 cm/s.
The formula for the instantaneous velocity of a particle at time t is found by differentiating the position function s(t).
cm
s'(t) = rhri7cQU6Zs=·t - iSba6t70dtA= 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
$2a0·t-$b = $vavg
t = qjqZz1N+poo= seconds
(Rounded to one decimal place)