Question

A body accelerates uniformly from rest to a velocity of $1m{s}^{-1}$ in $15$ second. The kinetic energy of the body will be $\frac{2}{9}J$ when ${}^{\prime }{t}^{\prime }$ is equal to [Take mass of body as $1kg]$

• A. 4 s
• B. 8 s
• C. 10 s
• D. 12 s

Answer 1

Answer: (C)

$a=\frac{v-u}{t}=\frac{1-0}{15}=\frac{1}{15}m/s^2$
$\Rightarrow v=\left(\frac{1}{15}\right)t$
$K=\frac{1}{2}m{v}^2;\frac{2}{9}J$
$=\frac{1}{2}(1kg){\left(\frac{1}{15}t\frac{m}{s}\right)}^2$
$\frac{2}{9}=\frac{1}{2}\cdot \frac{1}{15^2}\cdot t^2;t^2$
$=\frac{15^2\times 2^2}{9}$
$\Rightarrow t=\frac{15\times 2}{3}=10s$.