A) \[-5m\text{ }{{s}^{-2}},\text{ }2.5\text{ }N\text{ }s\]
B) \[-\text{ }10\text{ }m\text{ }{{s}^{-2}},\text{ }5\text{ }N\text{ }s\]
C) \[-\text{ }7.5\text{ }m\text{ }{{s}^{-2}},\text{ }3.5\text{ }N\text{ }s\]
D) \[-6m\text{ }{{s}^{-2}},\text{ }4\text{ }N\text{ }s\]
Correct Answer: A
Solution :
Here, \[m\text{ }=\text{ }2.5\text{ }kg,\text{ }v\text{ }=\text{ }1\text{ }m\text{ }{{s}^{-1}},\] \[s\text{ }=\text{ }10\text{ }cm\text{ }=\text{ }0.1\text{ }m\] Using, \[{{v}^{2}}={{u}^{2}}+2as\] or \[{{1}^{2}}=0+2(-a)\times 0.1\] or \[a=\frac{-10}{2}=-5m{{s}^{-2}}\] (negative sign indicates deceleration) We know, Impulse, \[I={{F}_{avg}}\times t=\]Final linear momentum- Initial linear momentum \[=m(v-u)=m(v-0)=2.5\times 1=2.5Ns\]
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