A particle starts from rest, moves with constant acceleration for $15 s$ . If it covers $s_{1}$ distance in first $5 s$ their distance $s_{2}$ in next $10 s$ , then find the relation between $s_{1}$ and $s_{2}$ .

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Solution

if acceleration be $a$ then using equation $S = u t + a t^{2} / 2$ and putting initial velocity $u = 0$ we get $s_{1} = a 5^{2} / 2 = 25 a / 2$ ..................... (1)
put $t = 15$ we get distance in $15 s e c o n d$ as $S = a 15^{2} / 2 = 225 a / 2$

Now distance travelled in $l a s t$ $10 s e c o n d s$ will be $distance in 15 second - distance in 5 second = S - s_{1} = 225 a / 2 - 25 a / 2 = 200 a / 2 = 100 a$
which is nothing but $8 \times 25 a / 2$ or $8 s_{1}$
So $s_{2} = 8 s_{1}$

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A particle starts from rest, moves with constant acceleration for 15s. If it covers s1 distance in first 5s their distance s2 in next 10s, then find the relation between s1 and s2.

A particle starts from rest, moves with constant acceleration for $15 s$ . If it covers $s_{1}$ distance in first $5 s$ their distance $s_{2}$ in next $10 s$ , then find the relation between $s_{1}$ and $s_{2}$ .