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The graphs in (i) and (ii) show the S-t ...

The graphs in (i) and (ii) show the S-t graph and V -t graph of a body. Are the motions shown in the graphs represented by OAB the same ?

Text Solution

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The motion shown by the two graphs are not same.
i) In the given `s-t` graph OA, is a uniform retardation motion.
Here, displacement = (average velocity) `xx` (time)
`therefore 10=((u+0)/(2))xx4`
`therefore u=5ms^(-1)`
using `v^(2)-u^(2)=2as`
`0-5^(2)=2a(10)`
`a=-1.25ms^(-2)`
ii) In the given `V-t` graph,
OA is a uniform retardation of motion
a = slope of the line `=(OA)/(OB)=(-4ms^(-1))/(4s)=-1ms^(-2)`
Thus the two graphs even though represent uniform retardation motions, the magnitudes are not equal.
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