Question

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it,given by the relation $s=\frac{1}{2}{t}^2$ , where t is in seconds. Work done by the force in 2 seconds is:-

• A. $\frac{5}{19}$ J
• B. $\frac{3}{8}$ J
• C. $\frac{8}{3}$ J
• D. $\frac{19}{5}$ J

Answer 1

The correct option is C $\frac{8}{3}$ J

By using work energy theorem
W = $\Delta$KE = $\frac{1}{2}m{v}_2^2$ - $\frac{1}{2}m{v}_1^2$

Now s = $\frac{1}{3}{t}^2\Rightarrow$ v = $\frac{2}{3}t$

$\Rightarrow$ v${}_1$ = 0, v${}_2$ = $\frac{2}{3}\times$ 2 = $\frac{4}{3}$ ms${}^{-1}$

Therefore W = $\frac{1}{2}\times$ 3${\left(\frac{4}{3}\right)}^2$ - $\frac{1}{2}\times$ 3 $\times {\left(0\right)}^2$ = $\frac{8}{3}$