Question:
A body starts slipping down an incline and moves half meter in half second. How long will it take to move the next half meter?
Solution:
In the first half metre,
$\mathrm{u}=0 \mathrm{~m} / \mathrm{s}, \mathrm{s}=0.5 \mathrm{~m}, \mathrm{t}=0.5 \mathrm{~s}$
$v=0+(0.5 \times 4)=2 \mathrm{~m} / \mathrm{s}$
$s=u t+1 / 2 a t^{2}$
$0.5=0+12(a)(0.5)^{2}$
$\mathrm{v}=\mathrm{u}+\mathrm{at}$
For the next half metre, $u=2 \mathrm{~m} / \mathrm{s}, \mathrm{a}=4 \mathrm{~m} / \mathrm{s}^{2}, \mathrm{~s}=0.5 \mathrm{~m}$
$0.5=2 t+(1 / 2)(4) t^{2}$
On solving, t=0.2027 sec
Time taken to cover the next half metre is $0.21 \mathrm{~s}$.
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