Question

A particle of mass $m$ accelerating uniformly has velocity $v$ at time $t_1$. What is work done in time $t$?

• A. $\frac{1}{2}\frac{m{v}^2}{t_1^2}{t}^2$
• B. $\frac{1}{2}{\left(\frac{m}{t_1}\right)}^2{t}^2$
• C. $\frac{m{v}^2}{t_1^2}{t}^2$
• D. $\frac{2m{v}^2}{t_1^2}{t}^2$

Answer 1

The correct option is A $\frac{1}{2}\frac{m{v}^2}{t_1^2}{t}^2$

Given that $v=a{t}_1$
$\therefore a=\frac{v}{t_1}$
Let at any time $t$ speed be $v^{\prime }$
Hence from work energy theorem
$W=\frac{1}{2}m{v}^{\prime 2}=\frac{1}{2}m(at{)}^2$

$=\frac{1}{2}m{(\frac{v}{t_1}\times t)}^2$

$=\frac{1}{2}m\frac{v^2{t}^2}{t_1^2}$