A particle is moving along the x-axis. Consider it’s a-t graph. If initial velocity is 10 m//s, sketch the v-t graph and calculate the displacement in the time interval t=0 to 12 s.

Explanation

At `t=0, v_(t=10)=10 m//s`
`v_(t=2)-v_(t=0)=Area(1)=20implies v_(t=2)-10=20impliesv_(t=2)=30 m//s`
`v_(t=4)-v_(t=2)=Area(2)=-10implies v_(t=4)=20 m//s`
`v_(t=6)-v_(t=4)=Area(3)=40implies v_(t=6)=60 m//s`
`v_(t=12)-v_(t=6)=Area(4)=-60implies v_(t=12)=0`

Area(1)`=1/2(10+30) 2=40`
`Area(2)=1/2(30+20)xx2=50`
Area(3)`=1/2(20+60) xx2=80`
Area(4)`=1/2xx60+6=180`
From `t=0` to `t=12 s`,
Displacement`=40+50+80+180=350 m`