Shows a graph of the acceleration of a model railroad locomotive moving on the x-axis. Graph its velocity and coordinate as functions of time if `x=0` and `v_(x)=0` at `t=0`.
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Answer

N//S

Explanation

At `t=5 s, v_(1)=u+at=0+2xx5 =10 ms^(-1)`
At `t=15 s, v_(1)=10 ms^(-1)`
At `t=25 s, v_(2)=v_(1)+ at =10-2xx10 =- 10 ms^(-1)`
At `t=35 s, v_(2)=-10 ms^(-1)`
At `t=40 s, v_(3)=v_(2)+ at=- 10 2xx5 0 ms^(-1)`
To find `x` ,
For `0` to `5` s, `x=(1)/(2) xx2xx5^(2)=25 m`
For `5` to `15`, `x=25+10xx10=125 m`
For `15` to `20, x=125 +v_(1)t+(1)/(2) at^(2)`
`=125+10xx(1)/(2) (-2)5^(2) =150 m`
For `20` to `25` s, `x=150+ 0xx5 +(1)/(2) (-2) 5^(2) =125 m`
For `25` to `35 s, x=125 +v_(2)t=125-10xx10=25 m`
For `35` to `40 s`, `x=25+v_(2)t+(1)/(2) at^(2)`
`12-10xx5+(1)/(2) xx2xx5^(2)=0`
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