A particle starts from rest and accelerated as shown in the graph. Determine
(a). The particle's speed at `t=10s` and at `t=20 s`
(b). The distance travelled in the first `20s`.

Explanation

(a). Upto 10 sec the particle moves with uniform acceleration hence the velocity at `t=10s`
`v_(1)=u+at=0+2x10=20 m//s`
From `t=10s` to `t=15s` the acceleration is zero, so the velocity of the particle at `t=15s` is `20 m//s`
Velocity at `t=20sec,v_(2)=v_(1)+at`
`=20+(-3)5=5 m//s`
(b). Distance travelled in first 10 sec
`s_(1)=ut+(1)/(2)a_(1)t^(2)=0xx10xx(1)/(2)xx2xx(10)^(2)=100m`
Distance travelled when `t=10sec` to `t=15sec`
`s_(2)=vt=20xx5=100m`
Distance travelled when `t=15sec` to `t=20sec`
`s_(3)=20xx5+(1)/(2)xx(-3)xx5^(2)=62.7m`
Total distance travelled in 20 sec `=s_(1)+s_(2)+s_(3)=100+100+2.5=262.5m`