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Q.

A particle moving with a constant acceleration describes in the last second of its motion 9/ 25^th of the whole distance. If it starts from rest, how long is the particle in motion and through what distance does it move if it describes 6 cm in the first sec.?

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a

15 s ; 100 cm

b

5 s; 150 cm

c

None

d

10 s ; 150 cm

answer is A.

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Detailed Solution

u = 0
$\frac{s_{n}}{s} = \frac{2 n - 1}{n^{2}} = \frac{9}{25}$
$\Rightarrow$ n= 5
u = 0 $\Rightarrow$ s $\propto$ t²
$\begin{aligned} \frac{s_{1}}{s_{2}} = {(\frac{t_{1}}{t_{2}})}^{2} \\ \frac{6}{s_{2}} = {(\frac{1}{5})}^{2} \end{aligned}$
s₂ = 6 × 25 = 150cm

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