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.
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Suppose at point `P` of the `st` graph both `a_(av)` and `vec v` areequal. The average velocity during time `t` is given by the slope of the line `QP` That means, by referring to the `s-t` graph ,
`b_(av)=(s_(1)-s_(0))/(t_(0))`
On the other hand, the velocity `v` of cockroach at the time `t` is at `P`. Hence. the point `P` has cordinates `3 m,3m`.
I t gemes `v_(av)=v =(Delta)/(Delta)=(2)/(3) ms^(-1)`.