Question

A particle covers 8 m distance in first three seconds and then covers a distance of 8 m in next two seconds. Find its velocity at t = 5 second.

• A. $\frac{32}{15}$ $m/s$
• B. $\frac{68}{15}$ $m/s$
• C. $\frac{34}{15}$ $m/s$
• D. $\frac{21}{15}$ $m/s$

Answer 1

The correct option is B $\frac{68}{15}$ $m/s$

Let initial speed of particle is $u$. Accleration is $a$.
$S=ut+\frac{1}{2}a{t}^2$
$8=3u+\frac{1}{2}a\left(3{)}^2\right\}$ first three seconds
$16=5u+\frac{1}{2}a\left(5{)}^2\right\}$ first five seconds

$40=15u+\frac{1}{2}a(3{)}^{2}5$
$48=15u+\frac{1}{2}a(5{)}^{2}3$
______________________
$8=\frac{a}{2}\left(75-45\right)=30\frac{a}{2}=15a$
$\Rightarrow a=\frac{8}{15}$
$8=3u+\frac{1}{2}a\left(3^2\right)$
$3u=8-\frac{36}{15}=8-\frac{12}{5}=\frac{28}{5}$
$u=\frac{28}{15}$
$v=u+at=\frac{28}{15}+\frac{8}{15}\times 5=\frac{28+40}{15}=\frac{68}{15}$