a particle is moving in a straight line such that its velocity varies is given by `v=10-2t`, where v isin the first 8 second.

Explanation

This problem can be solved by drawing the v-t graph.
`v=10-2t`
`t=0, v=10 m//s`
`t=8 s, v=-6 m//s`
`v=0implies10-2t=0impliest=5 s`
Shape: `y=10-2x` (straight line)
`y=c+mx`
`c=10`, +ve
`m=-2`, -ve

`Area(1)=25, Area(2)=9`
The area of the v-t graph gives the displacement//distance
Displacement`=25-9-16 m`
Displacement`=25+9=34 m`