A particle is moving along the x-axis and its velocity-time graph ia as shown in the following diagrems. Sketch the displacement-time graph.

Explanation

`Area(1)=10, Area(2)=20, Area (3)=20`
`t=0` to `t=2s`, Displacement`=10 m`
`t=0` to `t=4s`, Displacement`=30 m`
`t=0` to `t=8s`, Displacement`=50 m`

(b)
`Area(1)=12, Area(2)=12, Area(3)=-3, Area(4)=-9`
`t=0` to `2s`, Displacement`=12 m`
`t=0` to `4s`, Displacement`=24 m`
`t=0` to `5 s`, Displacement`=21 m`
`t=0` to `8s`, Displacement`=12 m`
Acceleration:
`t=0` to `t=2 s`, `a= 6 m//s^(2)`
`t=2` to `t=5 s`, `a= -6 m//s^(2)`
`t=5` to `t=8 s`, `a= 2 m//s^(2)`
`t=0` to `2s`, `v gt 0`, slope is +ve
` v gt 0, a gt 0`, speeding up, slope is increasing
`t=2` to `4s`, v gt 0, slope is +ve
`v gt 0, a lt 0`, slowing down, slope is decreasing
`t=4` to `5s`, v lt 0, slope is -ve
`v lt 0, a lt 0`, speeding up, slope is decreasing
`t=5` to `8s,` v lt 0, slope is -ve
v lt 0, a gt 0, slowing down, slope is increasing
`t=4s , v=0`, slope is zero, direction of motion is changing

(c )
`Area(1)=12, Area(2)=24, Area(3)=12, Area(4)=-3 Area(5)=-9, Area(6)=36`
`t=0` to `t=2 s`, Displacement`=12 m`
`t=0` to `t=4 s`, Displacement`=36 m`
`t=0` to `t=6s`, Displacement`=48 m`
`t=0` to `t=7 s`, Displacement`=45 m`
`t=0` to `t=10 s`, Displacement`=36 m`
`t=0` to `t=16 s`, Displacement`=72 m`