# Question #dea10

Dec 26, 2016

Considering rectilinear motion of the body with initial velocity $u$ and uniform acceleration $a$

As the body travels $1.8 m$ in first 3sec

$1.8 = u \cdot 3 + \frac{1}{2} \cdot a \cdot {3}^{2}$
$\implies 0.6 = u + 1.5 a \ldots . . \left[1\right]$

As the body travels $4 m$ in first 8sec

$1.8 + 2.2 = 4 = u \cdot 8 + \frac{1}{2} \cdot a \cdot {8}^{2}$

$\implies 0.5 = u + 4 a \ldots \ldots . \left[2\right]$

Subtracting [1] from[2]

$2.5 a = 0.5 - 0.6 = - 0.1$

$\implies a = - 0.04 m {s}^{-} 2$

Inserting $a = - 0.04$ in [2]

$0.5 = u - 4 \cdot \left(0.04\right)$

$\implies u = 0.66 m {s}^{-} 1$

velocity at the end of 9 sec
using equation $v = u + a t$

$v = 0.66 - 0.04 \cdot 9 = 0.66 - 0.36 = 0.3 m {s}^{-} 1$