First slide

Rectilinear Motion

Question

A particle moving with a constant acceleration describes in the last second of its motion $\frac{9}{25} t h$ of the whole distance. If it starts from rest, how long is the particle is motion.

Moderate

A

15s
B

5s
C

10s
D

20s

Solution

Given $u = 0$
$s_{n} = \frac{9}{25} s$
From equation $s_{n} = u + a (n - \frac{1}{2})$
$\Rightarrow \frac{9}{25} s = a (n - \frac{1}{2}) ............ (1)$
$∴$ But the total distance travelled in ‘n’ sec is
$\begin{array}{l} s = u (n) + \frac{1}{2} a (n)^{2} \\ = 0 + \frac{1}{2} a (n)^{2} \dots \dots . . . (2) \\ From (1) and (2) \\ ∴ \frac{9}{25} (\frac{1}{2} a n^{2}) = a \frac{(2 n - 1)}{2} \\ \Rightarrow \frac{9}{25} = (\frac{2 n - 1}{n^{2}}) \\ \Rightarrow n = 5 \sec \end{array}$

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