The position verus time graph time graph for a certain particle moving along the x-axis is shown in . Find the average velocity in the time intervals (a) `0` to `2s,` (b) `2 s` to `4 s`, and (c) `4,s` to `7 s`,
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Explanation

We are given the values of time, but the values of the position are to obtained from the graph correspondin to the given time interval under consideration. We know that the sope of the displacement -time graph represents velocitt.
Formula to be used: `v_(av)=(x_(2)-x_(1))/(t_(2)-t_(t))`, where `x_(1)` and `x_(2)` are the initial and final values of time, respitions, respectively, and `t_(1)` and `t_(2)` are the initial and final values of time, frspectively.
a. Here `x_(1)=10 m, x_(2)=5 m,t_(1)=2,.t_(2)=4 s`.
Therfore, the requited average velocity is giben by
`v_(ab)(10-0)/(2-0)= m s^(-1)`
b. Here `x_(1)=10 m,x_(2)=5 m,t_(1)=2 s, t_(2)=4 s`.
So the repuired value of average velocity is given by
`v_(av)=(5-10)/(4-2)=-2.5 m s^(-1)`
c. Here `x_(1)=5 m, x_(2)=-5 m, t_(1)=4 s, t_(2)=7 s`.
So the repuired value of average velocity is given by
`v_(av)=(-5-5)/(7-4)=(-10)/(3)=-3.3 ms^(-1)`.