The v-s graph for an airplane travelling on a straight runway is shown. Determine the acceleration of the plane at `s = 50 m` and `s = 150 m`. Draw the a-s graph.

Answer

A

Explanation

`a=v (dv)/(dx)=v` (slope of v-s graph)
At `s=50m`
`v=20 m//s` and `(dv)/(ds)=40/100=0.4` per sec
`:. a=20xx0.4=8 m//s^2`
At `s=150 m`
`v=(40+50)=45 m//s`
and `(dv)/(ds)=10/100=0.1` per sec
`:. a=45xx0.1=4.5 m//s^2`
a-s graph
From `s=0` to `s=100m v=0.4s`
and `(dv)/(ds)=0.4`
`:. a=v.(dv)/(ds)=0.16s`
i.e a-s graph is a straight line passing through origin
of slope `0.16` per `(sec)^2.`
At `s=100m,=0.16XX100=16 m//s^2`
From `s=100m` to `s=200 m`
`v=0.1s+30`
`(dv)/(ds)=0.1`
`:. a=v(dv)/(ds)=(0.1s+30)(0.1)=(0.01s+3)`
i.e. a-s graph is straight line of slope `0.01 (sec)^-2` and
intercept `3 m//s^2.`
At `s=100m, a=4m//s^2`
and at `s=200m,a=5m//s^2`
Corresponding a-s graph is as shown in figure.