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A body slows down such that v^(2) is var...

A body slows down such that `v^(2)` is varying linearly with displacement 's' as shown in the Fig.4.5. Assuming rectiliear motion, find the :
(a) acceleration of the body
(b) speed of the body when it just cross `100 m`
(c) `v - s` group

Text Solution

Verified by Experts

(a) The slope of `v^(2) - s` graph, that is `(d(v^(2)))/(ds)` is equal to `(800 - 2400)/(200 - 80) = - (40)/(3) m//s^(2)`, obtained from the given
Since, `(d(v^(2)))/(ds) = 2a`
and `(d(v^(2)))/(ds) = - (40)/(3)`,
we have `a = (-20)/(3) m//s^(2)`
(b) From the graph, `(v^(2) - 2400)/(200 - 80) = (-40)/(3)`
This yields `v = 20 sqrt2 m//s`
(c) Considering a point `P (s, v^(2))` on the `v^(2) -s` graph, equation of AB is given by `(v^(2) - 2400)/(s - 80) = - (40)/(3)`. It yield `v = sqrt((40)/(3) (260 - s))` as plotted in Fig.4.58
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