Question

A particle travels $10\text{m}$ in first $5$ seconds and $10\text{m}$ in next $3$ seconds. Assuming constant acceleration, what is the distance travelled in next $2$ second?

• A. $8.3\text{m}$
• B. $9.3\text{m}$
• C. $10.3\text{m}$
• D. None of these

Answer 1

The correct option is A $8.3\text{m}$

For first ${}^{\prime }{5}^{\prime }$ sec,
$10=u\times 5+\frac{1}{2}a\times 5^2$
$4=2u+5a...\left(1\right)$

For first ${}^{\prime }{8}^{\prime }$ sec,
$20=u\times 8+\frac{1}{2}a\times 8^2$
$5=2u+8a...\left(2\right)$

solving equation $\left(1\right)$ and $\left(2\right)$
$3a=1\Rightarrow a=\frac{1}{3}{\text{m/s}}^2$
$\Rightarrow u=\frac{7}{6}\text{m/s},$
Displacement in next $2\text{sec}$ is
$S_{\text{next}2S}=S_{10}-S_8$
$=(\frac{7}{6}\times 10+\frac{1}{2}\times \frac{1}{3}\times {10}^2)-(10+10)=8.3\text{m}$