Interpret the following graph and answer the following-
a) Find acceleration between

1) A to B
[tex]:\implies \sf \dfrac{Distance(AB) }{Total \: time (AM)} [/tex]
[tex]:\implies \sf \dfrac{20 }{3 }[/tex]
[tex]:\implies \sf 6.7m/s ^{2} [/tex]

2) B to C
[tex]:\implies \sf \dfrac{Distance(BC) }{Total \: time (MN)} [/tex]
[tex]:\implies \sf \dfrac{0}{1 }[/tex]
[tex]:\implies \sf {0}[/tex]

3) C to D
[tex]:\implies \sf \dfrac{Distance(CD) }{Total \: time(MD) } [/tex]
[tex]:\implies \sf \dfrac{20}{1 }[/tex]
[tex]:\implies \sf 20m/s ^{2} [/tex]

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b) the average speed for the complete journey (1 to 7 second)
We know that ,
[tex]\sf :\implies Average \: speed = \dfrac{Total \: distance}{Total \: time}[/tex]

Method 1 :- firstly we will divided it into three parts as shown in the attachment
In 1st case AMB
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times Base \times Height[/tex]
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times 3 \times 20[/tex]
[tex]\sf :\implies 30[/tex]

In 2nd case BCMN
[tex]\sf :\implies Area = Length \times Base[/tex]
[tex]\sf :\implies Area = 20 \times 2[/tex]
[tex]\sf :\implies 40[/tex]

In 3rd case CDN
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times Base \times Height[/tex]
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times 1 \times 20[/tex]
[tex]\sf :\implies 10[/tex]
now it is given to us that the time is 1 to 7 secondHence ,
Time = 6 sec
Total speed = 30+40+10 = 80

[tex]\sf :\implies Average \: Speed = \dfrac{80 }{6 } [/tex]
[tex]\sf :\implies Average \: Speed = \dfrac{40 }{3 } [/tex]
[tex]\sf :\implies Average \: Speed = 13.3 \bar{3} \: m[/tex]
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Method 2 :-Area of trapezium = ABCD
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times (BC + AD) \times AB[/tex]
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times (2 + 6) \times 20[/tex]
[tex]\sf :\implies Area = \dfrac{1 }{2 } \times 8 \times 20[/tex]
[tex]\sf :\implies Area = 80[/tex]

now it is given to us that the time is 1 to 7 second
Hence ,
Time = 6 sec
Total speed = 80
[tex]\sf :\implies Average \: Speed = \dfrac{80 }{6 } [/tex]
[tex]\sf :\implies Average \: Speed = \dfrac{40 }{3 } [/tex]
[tex]\sf :\implies Average \: Speed = 13.3 \bar{3} \: m[/tex]