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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)xx4therefore 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 retadation motions,the magnitudes are not equal.
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