• # question_answer A body of mass 2 kg has an initial speed of 5 m/s. A force acts on it for some time in the direction of motion. The force-time graph is shown in figure. The final speed of body is A) 9.25 m/s.                      B) 5 m/s.   C)   14.31 m/s.        D)                4.25 m/s.

Correct Answer: C

Solution :

$F=\frac{dP}{dt}\Rightarrow dP=Fdt$ $\therefore$$\int_{{}}^{{}}{dP=\int_{{}}^{{}}{F\,dt}\Rightarrow \Delta \Pi }=\int_{{}}^{{}}{F\,dt}$ So the change in moment$\Delta P$is equal to the area under the curve $\therefore$$\Delta P=\frac{1}{2}\times 2\times 4+4\times 2+\frac{1}{2}(4+2.5)$$\times \,0.5+2.5\times 2$ $=4+8+\frac{6.5}{4}+5=18.625$ $\Rightarrow$${{P}_{2}}-{{P}_{1}}=18.625\,\Rightarrow \,{{P}_{2}}={{P}_{1}}+18.625$ $\therefore$$m{{v}_{2}}=m{{v}_{1}}+18.625$ $\Rightarrow$${{v}_{2}}={{v}_{1}}+\frac{18.625}{2}=5+\frac{18.625}{2}$ $=14.3125\,m/s.$ Hence, the correction option is (c).

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