A cockroach moves rectilinearly such that after sometime `t_(0)` let its (instantaneous) velocity be equal to its average velocity over that time. Referring to the `S Delta t` graph as shown in , for the motion of the cockroach, find the time `t_(0)` and the average velocity of the cockroach over the time `t_(0)`
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Explanation

since `v_(av) = v` (given), the ''slope of `QP =`slope of the tangent PR''. Hence, QPR is a straight line.
Suppose at point ''P'' of `s - t` graph, both `vec(v)_(av)` and `vec(v)` are equal. The average velocity during time `t` is given by the slope of the line QP.
That means, `v_(av) = (s_(1) - s_(0))/(t_(0))` by referring to this `s - t` graph. on the other hand, the velcoity v of cockroach at the time t is equal to the slope of `s - t` graph at the instant (point P), `vec(v) = (d vec(s))/(dt) -=` slope of the tangent PR at P.
since `vec(v)_(av)` and `vec(v)` are equal, the straight line QP must be tangential at P. Hence, the point P has coordinates (3, 3).
It gives `v_(av) = v (Delta s)/(Delta t) = (2 m)/(3 s) = 0.67 m//s`