Question Number 39756 by Rio Mike last updated on 10/Jul/18
$${A}\:{force}\:{F}\:=\:\mathrm{2}{t}\:\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\:{acts}\:{on} \\ $$$${a}\:{particle}\:{of}\:{mass}\:\mathrm{2}{kg}.\:{find} \\ $$$${the}\:{velocity}\:{and}\:{the}\:{magnitude} \\ $$$${of}\:{the}\:{impulse}\:{that}\:{acts}\:{on}\: \\ $$$${the}\:{particle}\:{within}\:{the}\:{time} \\ $$$${range}\:\:\mathrm{1}\boldsymbol{{s}}\:\leqslant\:\boldsymbol{{t}}\:\leqslant\:\mathrm{3}\boldsymbol{{s}} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 10/Jul/18
Answered by ajfour last updated on 10/Jul/18
$${m}\bar {{v}}\:=\bar {{J}}\:=\:\int_{\mathrm{0}} ^{\:\:{t}} \bar {{F}dt} \\ $$$$\mathrm{2}\bar {{v}}\:=\:{t}^{\mathrm{2}} \hat {{i}}+\mathrm{5}{t}\hat {{j}}\:=\bar {{J}}\: \\ $$$$\:\:{J}\:={t}\:\sqrt{{t}^{\mathrm{2}} +\mathrm{25}}\:. \\ $$