A) \[\frac{\sqrt{3}}{2}b,\,\,\frac{b}{2}\]and b respectively
B) \[\frac{b}{2},\,\,\frac{b}{2}\]and b respectively
C) \[\sqrt{2}b,\,\,\sqrt{2}b\]and b respectively
D) none of the above
Correct Answer: A
Solution :
| \[\overrightarrow{v}=a\overset{\hat{\ }}{\mathop{j}}\,+bt\overset{\hat{\ }}{\mathop{j}}\,;\,\]\[\therefore \,\,\,\,\,\,\overrightarrow{a}=b\overset{\hat{\ }}{\mathop{j}}\,\]; |
| Total acceleration =b; speed, \[v={{\left( {{a}^{2}}+{{b}^{2}}{{t}^{2}} \right)}^{1/2}}\] |
| Tangential acceleration |
| \[=\frac{dv}{dt}=\frac{1}{2}{{\left( {{a}^{2}}+{{b}^{2}}{{t}^{2}} \right)}^{-1/2}}\left( 2{{b}^{2}}t \right)\] |
| At\[\,\,\,\,t=\frac{\sqrt{3a}}{b}\]; Tangential acceleration\[t=\frac{\sqrt{3}b}{2}\] and normal acceleration \[=\sqrt{{{b}^{2}}-\frac{3{{b}^{2}}}{4}}=\frac{b}{2}\] |
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